Figure 1.
Peridynamic horizon and interaction between material points.
Peridynamics is a new approach to continuum mechanics. There has been rapid progress in peridynamics research, especially in recent years. In this review study, recent advances in peridynamics research were summarised. A large number of studies were considered and classified into different categories ranging from additive manufacturing, artificial intelligence and machine learning, composite materials, fatigue, functionally graded materials, impact, reduced order modelling, structural health monitoring, topology optimisation, and many more. Finally, some future directions were highlighted.
Citation: Erkan Oterkus, Selda Oterkus. Recent advances in peridynamic theory: A review[J]. AIMS Materials Science, 2024, 11(3): 515-546. doi: 10.3934/matersci.2024026
| [1] | Kai Friebertshäuser, Christian Wieners, Kerstin Weinberg . Dynamic fracture with continuum-kinematics-based peridynamics. AIMS Materials Science, 2022, 9(6): 791-807. doi: 10.3934/matersci.2022049 |
| [2] | Holm Altenbach, Oleksiy Larin, Konstantin Naumenko, Olha Sukhanova, Mathias Würkner . Elastic plate under low velocity impact: Classical continuum mechanics vs peridynamics analysis. AIMS Materials Science, 2022, 9(5): 702-718. doi: 10.3934/matersci.2022043 |
| [3] | Aylin Ahadi, Jakob Krochmal . Anisotropic peridynamic model—Formulation and implementation. AIMS Materials Science, 2018, 5(4): 742-755. doi: 10.3934/matersci.2018.4.742 |
| [4] | Yakubu Galadima, Erkan Oterkus, Selda Oterkus . Two-dimensional implementation of the coarsening method for linear peridynamics. AIMS Materials Science, 2019, 6(2): 252-275. doi: 10.3934/matersci.2019.2.252 |
| [5] | Ruby Maria Syriac, A.B. Bhasi, Y.V.K.S Rao . A review on characteristics and recent advances in piezoelectric thermoset composites. AIMS Materials Science, 2020, 7(6): 772-787. doi: 10.3934/matersci.2020.6.772 |
| [6] | K.A. Lazopoulos, E. Sideridis, A.K. Lazopoulos . On Λ-Fractional peridynamic mechanics. AIMS Materials Science, 2022, 9(5): 684-701. doi: 10.3934/matersci.2022042 |
| [7] | Erkan Oterkus, Timon Rabczuk, Selda Oterkus . Special Issue: Peridynamics and its applications. AIMS Materials Science, 2024, 11(3): 602-604. doi: 10.3934/matersci.2024030 |
| [8] | Bozo Vazic, Hanlin Wang, Cagan Diyaroglu, Selda Oterkus, Erkan Oterkus . Dynamic propagation of a macrocrack interacting with parallel small cracks. AIMS Materials Science, 2017, 4(1): 118-136. doi: 10.3934/matersci.2017.1.118 |
| [9] | Shashi Bahl, Tarunpreet Singh, Virinder Kumar, Shankar Sehgal, Ashok Kumar Bagha . A systematic review on recent progress in advanced joining techniques of the lightweight materials. AIMS Materials Science, 2021, 8(1): 62-81. doi: 10.3934/matersci.2021005 |
| [10] | Azhar Equbal, Ramesh Murmu, Veenit Kumar, Md. Asif Equbal . A recent review on advancements in dimensional accuracy in fused deposition modeling (FDM) 3D printing. AIMS Materials Science, 2024, 11(5): 950-990. doi: 10.3934/matersci.2024046 |
Peridynamics is a new approach to continuum mechanics. There has been rapid progress in peridynamics research, especially in recent years. In this review study, recent advances in peridynamics research were summarised. A large number of studies were considered and classified into different categories ranging from additive manufacturing, artificial intelligence and machine learning, composite materials, fatigue, functionally graded materials, impact, reduced order modelling, structural health monitoring, topology optimisation, and many more. Finally, some future directions were highlighted.
Peridynamics (PD) is a new formulation of continuum mechanics that was developed to overcome the limitations of classical continuum mechanics (CCM) [1]. Although CCM has been utilised for the analysis of numerous problems, it is challenged by discontinuities in the displacement field and/or its derivatives, since the governing equations of CCM contain derivatives with respect to space coordinates. On the other hand, equations of motion in PD theory do not have spatial derivatives and, therefore, do not suffer from issues related to discontinuities.
There has been significant progress in PD research, especially in recent years. A general overview of PD can be found in [2]. In this study, recent developments in PD theory are briefly described. Only journal papers published since 2019 were considered since previous ones were reviewed in a former study [3]. The current review is organised under different categories, which are listed in alphabetical
order; relevant studies are discussed. Note that due to the large number of publications available in the literature, only a selected set of publications is presented for each category.
The peridynamic theory is a nonlocal continuum mechanics formulation; its equation of motion can be expressed in Eq 1 as [4]
| ρ(x)¨u(x,t)=∫H(t(u′−u,x′−x,t)−t′(u−u′,x−x′,t))dH+b(x,t) | (1) |
Eq 1 can be rewritten in discrete form in Eq 2 as (see Figure 1):
| ρ(k)¨u(k)=∞∑j=1[t(k)(j)(u(j)−u(k),x(j)−x(k),t)−t(j)(k)(u(k)−u(j),x(k)−x(j),t)]V(j)+b(k) | (2) |
where ρ is the density of a material point, x is the original location of a material point, u represents the displacement of a material point, b is the body load of a material point, t is time, and ".." represents the second derivative with respect to time. Peridynamic force densities between two material points can be defined in Eq 3 as
| t(k)(j)(u(j)−u(k),x(j)−x(k),t)=12Ay(j)−y(k)|y(j)−y(k)| | (3) |
with Eq 4 as
| A=4w(k)(j){ad(y(j)−y(k)|y(j)−y(k)|⋅x(j)−x(k)|x(j)−x(k)|)θ(k)+b(|y(j)−y(k)|−|x(j)−x(k)|)} | (4) |
and in Eq 5
| t(j)(k)(u(k)−u(j),x(k)−x(j),t)=−12By(j)−y(k)|y(j)−y(k)| | (5) |
with Eq 6 as
| B=4w(j)(k){ad(y(k)−y(j)|y(k)−y(j)|⋅x(k)−x(j)|x(k)−x(j)|)θ(j)+b(|y(k)−y(j)|−|x(k)−x(j)|)} | (6) |
Note that y is the current location of a material point. The peridynamic dilatation term can be expressed in Eq 7 as
| θ(k)=d∞∑j=1w(k)(j)s(k)(j)y(j)−y(k)|y(j)−y(k)|⋅(x(j)−x(k))V(j) | (7) |
and the stretch term can be defined in Eq 8 as
| s(k)(j)=(|y(j)−y(k)|−|x(j)−x(k)|)|x(j)−x(k)| | (8) |
The influence function can be chosen in Eq 9 as
| w(k)(j)=δ|x(j)−x(k)| | (9) |
where δ represents the horizon size. The constants, a, b, and d can be expressed in Eqs 10–12, respectively, as
| a=12(κ−5μ3) | (10) |
| b=15μ2πδ5 | (11) |
| d=94πδ4 | (12) |
where κ is the bulk modulus and μ is the shear modulus. For brittle materials, if the stretch between two material points exceeds a critical stretch value, then it can be assumed that the bond (interaction) is broken. The critical stretch for isotropic materials can be obtained in Eq 13 as
| sc=√Gc(3μ+(34)4(κ−5μ3))δ | (13) |
where Gc is the critical energy release rate.
In this section, a large number of journal papers on peridynamics were organised under different categories, which are listed in alphabetical order.
Additive manufacturing is a new and promising manufacturing approach. Hartmann et al. [5] developed a model to simulate the extrusion-based additive manufacturing process of soft polymers using peridynamics. Karpenko et al. [6,7,8] investigated the influence of porosity and residual stresses on fatigue nucleation and crack propagation for additively manufactured titanium alloys based on peridynamic simulations. Kendibilir et al. [9] performed a peridynamic topology optimisation study for additive manufacturing with surface cracks. Zhu et al. [10] worked on a peridynamic buildability analysis of additively manufactured concrete by considering damage, plastic flow, and collapse.
Analytical solutions of peridynamic equations are very limited in the literature. Yang et al. [11] provided the analytical solution for one-dimensional problems. In another study [12], the analytical solution for a two-dimensional membrane was presented. Yang et al. [13,14] also derived analytical solutions for peridynamic beam and plate equations. Mikata [15] presented analytical solutions to linearised peridynamic equations for isotropic and anisotropic materials. Recently, they also provided analytical solutions for three-dimensional isotropic materials under both static and dynamic conditions [16].
Artificial intelligence and machine learning are emerging areas used in many different engineering applications. Kim et al. [17] utilised deep neural networks based on data generated by peridynamic simulations that significantly decreased the computational time for fracture problems. Nguyen et al. [18,19] developed peridynamic-based machine learning models for bond-based and ordinary state-based peridynamics. Bekar and Madenci [20] predicted terms in partial differential equations describing physical phenomena based on measured data and peridynamic differential operators. Xu et al. [21] utilised machine learning to determine a proper peridynamic material model for a particular problem. Ning et al. [22] developed a peridynamic-informed neural network and analysed the displacement field in heterogeneous elastic plates. Babu and Gopalakrishanan [23] presented a peridynamic-based machine learning model for thermal diffusion problems by considering cracks.
In many engineering applications, structures can be simplified by considering them as beams, plates, and shells. These simplifications can significantly reduce the computational time for full three-dimensional models. Peridynamic beam, plate, and shell formulations are also available in the literature. Nguyen et al. [24] presented a peridynamic beam formulation utilised for predicting damage in offshore structures. In another study [25], the authors investigated the thermomechanical behaviour of shell structures. Diyaroglu et al. [26] introduced a new formulation for Euler-Bernoulli beams in an ordinary state-based peridynamic framework. Yang et al. [27] explained how peridynamic beam and plate formulations can be implemented in commercial finite element software packages. They also presented peridynamic formulations for Timoshenko beams [28] and Kirchhoff plates [29]. Vazic et al. [30] investigated the case of a Mindlin plate resting on a Winkler elastic foundation. Oterkus et al. [31] presented a new formulation for peridynamic shell membranes. Yolum and Güler [32] derived a peridynamic formulation for orthotropic Mindlin plates subjected to bending loading. Nguyen and Oterkus [33,34] performed geometrically nonlinear analysis of beams and plates. Shen et al. [35] modelled peridynamic beams and shells by utilising the interpolation method and considering transverse shear effect. Yang et al. [36,37,38] introduced peridynamic formulations for Mindlin plates, higher-order beams, and higher-order plates. Zhang et al. [39] derived the peridynamic Reissner–Mindlin shell theory. Dai et al. [40] performed fracture parameter analysis of flat shells in an ordinary state-based peridynamic framework by considering out-of-plane loading conditions. In another study [41], the authors studied the utilisation of different horizon sizes for the analysis. Moreover, they investigated the fracture behaviour of cracked Mindlin plates under static and dynamic conditions [42]. Naumenko and Eremeyev [43] presented a nonlinear direct peridynamics plate theory. Behzadinasab et al. [44] introduced a new inelastic and rotation-free peridynamic Kirchhoff–Love shell formulation. Yang et al. [45] performed an analysis of peridynamic curved beams. Xia et al. [46] demonstrated the coupling of isogeometric analysis and peridynamics for peridynamic shells.
Buckling and free vibration analyses are important for the durability of structures. Heo et al. [47] utilised peridynamics to determine the natural frequency of cracked plates. Moreover, they also determined critical buckling loads by implementing peridynamics in a commercial finite element framework [48]. Yang et al. [49] performed buckling analysis of beams.
Coatings are widely utilised in many different industrial applications. Their durability is critical to the structure that coatings are attached to. Zhang et al. [50] utilised peridynamics to investigate the fracture behaviour of functionally graded coatings under dynamic conditions. Guski et al. [51] studied the microstructural behaviour of plasma-sprayed ceramic coatings. Vasenkov [52] performed multiphysics analysis to determine damage processes in protective coatings. Wang et al. [53] investigated the fracture behaviour of multilayer thermal barrier coatings. Wen et al. [54] developed a peridynamic model for coupled thermomechanical-oxygenic analysis of carbon/carbon composites with silicon carbide coating.
Composite materials are widely used in different areas due to their superior properties to traditional materials. Analysis of the fracture behaviour of composite materials is complex since various fracture modes can occur, such as delamination, fibre breakage, fibre-matrix splitting, etc. There are many peridynamic studies focused on the analysis of composite materials. Rädel et al. [55] utilised an energy-based damage criterion to investigate fibre-matrix debonding and matrix failure. Gao and Oterkus [56] developed a fully coupled thermomechanical model for composites and investigated the effect of shock loading. Hu et al. [57] introduced a peridynamic model for composite laminates by considering transverse shear deformation and material coupling. Postek and Sadowski [58] investigated the impact behaviour of aluminium oxide/zirconia composite. Basoglu et al. [59] studied how the toughness of unidirectional fibre-reinforced composites can increase by introducing microcracks. Li et al. [60] coupled peridynamics and finite element method to examine the fracture behaviour of composites. Yang et al. [61] developed a peridynamics-based statistical multiscale model to investigate fracture behaviour in composites. Madenci et al. [62] used peridynamics to predict failure in variable angle tow composites. Yang et al. [63] performed out-of-plane damage analysis of composites. Ma et al. [64] analysed interfacial failure in composite materials by using an extended peridynamic model and non-uniform discretization. Wang et al. [65] investigated the fracture mechanics of 2D orthotropic materials based on ordinary state-based peridynamics.
Kamensky et al. [66] developed a peridynamic model of frictional contact. Lu et al. [67] studied fracture due to Hertzian indentation. In another study, they modelled cracks with frictional contact [68]. Wang et al. [69] studied contact fatigue crack initiation and propagation. Zhang et al. [70] examined the sticking and sliding frictional contact by considering fracture. Mohajerani and Wang [71] presented a "touch-aware" frictional contact model suitable for simulating the contact behaviour between irregularly shaped particles. Guan et al. [72] introduced an adaptive contact model including friction. Zhu et al. [73] developed a peridynamic model to investigate stochastic fractures in bolted glass plates. Naumenko et al. [74] examined damage patterns in float glass plates by performing both experiments and peridynamic analysis.
Corrosion is a major challenge for structures subjected to corrosive environments, such as marine structures. There are various corrosion mechanisms, such as uniform corrosion, pitting corrosion, or stress corrosion cracking. Modelling corrosion based on physics and chemistry is complex. However, peridynamics can be a suitable approach to tackle this challenging problem. Rokkam et al. [75] developed a peridynamic model for corrosion damage and crack propagation. Nguyen and Oterkus [76] investigated brittle damage in corroded stiffened structures subjected to static loading conditions. Karpenko et al. [77] studied corrosion fatigue crack growth rates for titanium alloys. Jafarzadeh et al. [78] utilised peridynamics to model crevice corrosion. Tan et al. [79] performed crack analysis of atmospheric stress corrosion. Wang et al. [80] investigated corrosion fatigue crack growth in stainless steel. Zhou et al. [81] developed a peridynamic model suitable for electrochemical and stress chemical corrosion by establishing a coupled chemomechanical framework.
Small-size defects such as microcracks and pores that can occur at the microstructure can have a significant influence on the overall fracture behaviour of the material and structure. Peridynamics is a suitable tool to analyse such defects and their influence on the material and structure. Basoglu et al. [82] demonstrated how to change the direction of crack propagation by using microcracks. Karpenko et al. [83] studied the effect of various kinds of small defects on crack propagation in brittle materials. Rahimi et al. [84] showed how to increase the toughness of brittle materials by drilling stop-holes. Candas et al. [85] presented how macro and microcracks interact with each other under impact-loading conditions. Wang et al. [86] developed a mesoscale model to investigate the influence of micro-void defects on the transverse mechanical properties of composites. Ozdemir et al. [87] performed an in-depth investigation on the macro–microcrack interactions for functionally graded materials.
Peridynamics is a very suitable approach for dynamic fracture analysis of materials and structures. Such conditions can lead to sophisticated fracture patterns such as branching and fragmentation, which can be easily captured by peridynamics demonstrating the superior features of peridynamic methodology. For instance, Cheng et al. [88] performed dynamic fracture analysis of shale. Imachi et al. [89] studied dynamic crack arrest analysis by using ordinary state-based peridynamics. Butt and Meschke [90] investigated the influence of horizon, dimensionality, and specimen size for peridynamic dynamic fracture analysis. Yang et al. [91] coupled the boundary element method and bond-based peridynamics to examine dynamic crack propagation.
Peridynamics has been mainly introduced for failure prediction in materials and structures. To make accurate failure predictions, it is critical to use a suitable failure criterion depending on the material and loading. There are several failure criteria available in the literature for different conditions. Imachi et al. [92] introduced a new failure criterion named "new transition bond" that eliminates oscillations for dynamic stress intensity factors. Jiang et al. [93] utilised energy-based failure criteria to predict the open-hole tensile strength of fibre-reinforced composites. Karpenko et al. [94] did a detailed study to determine the most suitable critical stretch-based failure criterion in an ordinary state-based peridynamic framework. Silling [95] investigated the dynamic behaviour of an elastic material by considering a nonconvex potential and incubation time for the nucleation of a crack. Wang et al. [96] presented fracture predictions in brittle materials using a strength-induced peridynamic model. Kumagai [97] defined a parameter corresponding to stress triaxiality in CCM and used it for a fracture criterion in an ordinary state-based peridynamic framework. Ignatiev et al. [98] presented a peridynamic formulation of the mean stress and incubation time fracture criteria.
Fatigue is one of the most common and dangerous damage mechanisms that structures experience under cyclic loading conditions. Fatigue calculations are mostly done based on traditional S-N curves and Paris law approaches. Although these are useful techniques, they have certain limitations. The peridynamic fatigue model can be a very suitable alternative approach to these traditional techniques. Ma et al. [99] developed a peridynamic model to predict fatigue crack initiation in railheads. Han and Chen [100] presented the fatigue cracking of ferrite and pearlite wheel materials. Nguyen et al. [101] introduced a peridynamic fatigue model suitable for fatigue crack growth prediction subjected to overload and underload. Hong et al. [102] simulated fatigue crack growth in fillet welded joints. Bang et al. [103] provided an analytical solution approach for the peridynamic fatigue model. Zhu et al. [104] performed fatigue analysis of polycrystalline materials by introducing a new crack tip detection algorithm. Nguyen et al. [105] developed an energy-based peridynamic fatigue model. Binchao et al. [106] introduced a cumulative peridynamic fatigue damage model. Li et al. [107] presented a fatigue model for non-ordinary state-based peridynamics suitable for low-cycle cases. Hamarat et al. [108] performed a fatigue damage assessment of complex railway turnout crossings. Zhang and Madenci [109] implemented a coupled peridynamic and finite element fatigue life prediction approach in ANSYS framework by using the kinetic theory of fracture. Cao et al. [110] developed a peridynamic fatigue model for composites for non-ordinary state-based peridynamics. Cruz and Donadon [111] presented a peridynamic mixed-mode energy-based fatigue model by considering elastoplastic material behaviour. Bang and Ince [112] integrated the peridynamic fatigue model with a two-parameter crack driving force. Nguyen et al. [113] investigated fatigue crack growth in ceramic materials and porous media. Wang et al. [114] studied mixed-mode fatigue crack growth in an ordinary state-based framework. Ni et al. [115] introduced a peridynamic fatigue model for composites. Altay et al. [116] presented a peridynamic fatigue model suitable for functionally graded materials. Chen et al. [117] performed fatigue crack growth analysis of hydrogels. Cheng et al. [118] investigated the fatigue behaviour of engineered cementitious composites. Zhang and Chen [119] developed a peridynamic fatigue model suitable for spectrum loadings.
Although peridynamics was originally introduced for structural analysis, it is now used for the analysis of other physical fields including fluid flow modelling. It can also be used for the analysis of fluid-structure interactions, which can be especially important for aerospace and maritime fields. Gao and Oterkus [120] utilised a peridynamic differential operator to simulate low Reynolds number laminar fluid flow. Mikata [121] derived peridynamic equations of fluid mechanics for barotropic flow. Nguyen et al. [122] developed a peridynamic model for incompressible fluids by using the Eulerian approach. Kim et al. [123] introduced a peridynamic model for fluid-structure interaction problems with damage prediction capability. Wang et al. [124] presented a peridynamic model to simulate multiphase flow wetting and thermocapillary flow.
As additive manufacturing methods are advancing, manufacturing materials with varying properties has become a reality. Having such characteristics, functionally graded materials can be a good alternative to composites, mitigating the risk of delamination failure problems. Cheng et al. [125,126] investigated dynamic fracture in functionally graded materials. Dorduncu [127] performed stress analysis of sandwich plates with functionally graded cores by utilising refined zigzag theory. Ozdemir et al. [128] studied the fracture behaviour of functionally graded materials under dynamic loading conditions. Yang et al. [129,130,131,132,133,134] provided formulations for functionally graded Euler–Bernoulli beams, Mindlin plates, Timoshenko beams, Kirchhoff plates, higher-order beams, and higher-order plates. He et al. [135] performed fracture analysis of functionally graded materials subjected to shock loading. Dorduncu et al. [136] developed a peridynamic model for functionally graded plates. Wang et al. [137] determined fracture parameters for functionally graded materials. Candas et al. [138,139] investigated the impact behaviour of functionally graded materials with or without microcracks. Jiang et al. [140] utilised element-based peridynamics to analyse orthotropic functionally graded materials.
One of the main advantages of peridynamics is its capability to be used for modelling materials at a small scale. Its length scale parameter, the horizon, can allow capturing physical phenomena mainly occurring at small scales. Celik et al. [141] determined the elastic moduli of polymer thin films by numerically simulating the nanoindentation process. Liu et al. [142] studied the fracture behaviour of single-layer graphene sheets with preexisting cracks. In another study, Liu et al. [143] developed a peridynamic model depending on chirality for analysing fractures in graphene sheets. Silling and Fermen-Coker [144] introduced a peridynamic model to simulate the microballistic perforation of multilayer graphene. Torkaman-Asadi and Kouchakzadeh [145] used peridynamics for the analysis of pre-cracked graphene layer sheets. Liu et al. [146] examined the fracture behaviour in polycrystalline graphene. Silling et al. [147] developed a peridynamic model for single-layer graphene based on coarse-grained bond forces. Liu et al. [148] utilised peridynamics to determine the mechanical and fracture properties of graphene. Liu et al. [149] investigated fractures in multi-layer graphene sheets.
For materials having periodic microstructures, it is important to determine homogenised properties to reduce computational time. Peridynamics allows the determination of such properties during the existence of microdefects such as micro-voids and microcracks. Xia et al. [150] performed representative volume element homogenisation of a composite material within a bond-based peridynamics framework. Diyaroglu et al. [151] performed peridynamic homogenisation in a finite element framework for microstructures with orthotropic components. Buryachenko [152] presented the computational homogenisation of composites with periodic microstructure by considering linear elasticity and static conditions. Galadima et al. [153] studied the influence of inclusion shapes on homogenised properties. Xia et al. [154] demonstrated a peridynamic model suitable for materials with periodic microstructure. Eriksson and Stenström [155] demonstrated a one-dimensional homogenisation process by considering triangular micromodulus. Xia et al. [156] presented a three-dimensional representative volume element homogenisation for bond-based peridynamics. In another study [157], the authors explained the homogenisation process of periodic microstructure materials in an ordinary state-based peridynamic framework. Buryachenko [158] presented the computational homogenisation of composite materials with periodic microstructure. Li et al. [159] utilised improved bond-based peridynamics for homogenisation based on representative volume elements. Galadima et al. [160,161] performed computational homogenisation for viscoelastic composites to investigate the influence of phase contrast and inclusion shape on homogenised properties. In another study [162], they considered the effect of changing microstructure and damage. They also explained how computational homogenisation can be done in a non-ordinary state-based peridynamic framework [163]. Buryachenko [164] used a generalised Mori-Tanaka methodology for the homogenisation of multilayered composites with random structures. Qi et al. [165] performed peridynamic homogenisation by utilising a peridynamic differential operator to obtain the displacement gradient and stress field.
As mentioned earlier, peridynamics has a length scale parameter, called horizon, which defines the range of interactions between material points. Several studies have investigated different aspects of peridynamics. Oterkus et al. [166] studied the influence of the shape of the horizon in peridynamics by considering circular, irregular, and square shape horizons. Vazic et al. [167] investigated an important aspect of the numerical implementation of peridynamics, which is related to the determination of material points inside the horizon of a material point, i.e., family members. They compared different algorithms to determine the most efficient algorithm for family member search purposes. Wang et al. [168] demonstrated how to determine horizon size in state-based peridynamics.
The study of ice–structure interactions is an important field of engineering. In the Arctic region, ice and structures interact with each other in different forms. One common application is ship and ice interactions. The Arctic can serve as a potential ship route for the transportation of products from the Far East to Europe. Another important application is offshore platforms and their interaction with ice, especially during winter time. The material behaviour of ice is very complex and depends on many factors. During ice–structure interactions, while ice may be fracturing, it can also apply a significant load on the structure, which can cause damage to the structure. The consequences can be significant as in the well-known Titanic accident due to the impact of an iceberg on the ship's hull. Peridynamics can play an important role in representing the ice–structure interaction process. Song et al. [169] studied ice fragmentation due to impact loading by using non-ordinary state-based peridynamics. Ye et al. [170] simulated the submarine surfacing through ice. Vazic et al. [171] utilised peridynamics to investigate the in-plane and out-of-plane failure of an ice sheet. Liu et al. [172] presented an ice–water interaction model by coupling peridynamics and updated Lagrangian particle hydrodynamics. Lu et al. [173] introduced a peridynamic model for the fracture analysis of polycrystalline ice. Liu et al. [174] used micropotential-based peridynamics to study model-scale ice. Chunyu et al. [175] utilised peridynamics to simulate a dynamic ice-milling process. Zhang et al. [176] investigated the effect of rigid ball impact on ice plate fracture. Song [177] developed a thermomechanical peridynamic model for inhomogeneous ice fracture. Xiong et al. [178] simulated the impact process by considering spherical ice and rigid plate. Zhang et al. [179] studied the computational efficiency of peridynamics for ice–structure interaction modelling.
The peridynamic equation is defined to describe the evolution of materials and structures in time due to external loading conditions. Therefore, peridynamics is very suitable for predicting dynamic cases. An important dynamic scenario is impact condition and damage patterns emerging as a result of impact phenomenon. There are numerous studies in the literature focusing on impact analysis by using peridynamics. Rivera et al. [180] investigated the effect of the ballistic impact on glass fracture. Kazemi et al. [181] examined plasticity behaviour occurring during high-velocity impact cases. Ha [182] introduced an extended ghost interlayer model to study high-velocity impact fracture of laminated glass structures. Altenbach et al. [183] compared classical continuum mechanics and peridynamics for an elastic plate subjected to low-velocity impact loading. Zheng et al. [184] predicted failure characteristics of a reinforced concrete T-beam under impact loading. Wu and Huang [185] proposed a new elastoplastic contact model for low and high-speed impact conditions. Jafaraghaei et al. [186] simulated damage in glass plates due to impact loading. Candas et al. [187] analysed the impact behaviour of wire ropes subjected to transverse loading. Xu et al. [188] studied damage evolution in carbon fiber-reinforced plastic (CFRP) due to multiple impacts. Zhang et al. [189] developed an elasto-viscoplastic peridynamic model to investigate brittle and ductile fractures due to high-velocity impact loading. In another study, Lu et al. [190] performed viscoelastic peridynamic fracture analysis for concrete beams with preexisting cracks subjected to impact loading conditions. Cheng et al. [191] examined the impact behaviour of engineering cement-based composite materials.
One of the main advantages of peridynamics is its capability to represent interfaces between two different material systems. This can be done by assigning different properties for the peridynamic interactions (bonds) passing through interfaces. Alebrahim [192] investigated Lamb wave propagation in bimaterial plates. Nguyen et al. [193] examined interface modelling in an ordinary state-based peridynamic framework. Zhang et al. [194] introduced a modified critical energy density criterion to represent the failure of interface bonds. Wu et al. [195] performed a fracture analysis of Ni/Ni3Al bimaterial structure. Wang et al. [196] utilised extended peridynamics to study interfacial and subinterfacial crack propagation. Masoumi et al. [197] developed modified bond-based peridynamics to investigate viscoelastic-elastic interfaces.
In addition to the application of peridynamics for different purposes by considering different loading and material systems, there have also been fundamental developments in peridynamic formulation. Liu et al. [198] introduced element-based peridynamics by defining interactions (bonds) by using elements. Imachi et al. [199] proposed a smoothed variable horizon peridynamic formulation by introducing a smoothing length between different scale particle distributions to eliminate the effect of "ghost" forces. Xia et al. [200] combined isogeometric analysis and peridynamics to utilise the benefits of both approaches. Javili et al. [201] developed a geometrically exact formulation of peridynamics that is suitable for large deformations and variationally consistent. Yang et. al. [202] proposed a double-horizon peridynamic formulation by using two horizons instead of one as in the original peridynamic formulation, which can lead to a computational efficiency of peridynamic simulations with larger horizon sizes. Wang et al. [203] demonstrated that dual horizon state-based peridynamic formulation can be obtained using the Euler–Lagrange equation. Chen et al. [204] introduced a bond-associated correspondence formulation. They derived a bond-associated deformation gradient, eliminating the need for zero-energy-mode stabilisation and allowing for a more straightforward implementation of existing damage models [205]. Jafarzadeh et al. [206] introduced a fast convolution-based method for peridynamics. By using Fourier transforms, they significantly reduced the computational complexity of peridynamics simulations and greatly improved the simulation time and memory consumption.
Peridynamics is not limited to macroscopic analysis. In some cases, microstructural behaviour can have a significant influence on macroscopic behaviour. In such cases, it could be necessary to incorporate microstructural details in the peridynamic model. For certain material systems such as metals, ceramics, ice, etc., crystals should be considered as part of the microstructure. To represent crystals, it is critical to develop a corresponding material model in the peridynamic framework. Gu et al. [207] simulated a fracture of polycrystals under dynamic conditions by using non-ordinary state-based peridynamics. Gur et al. [208] investigated the influence of grain size on the fracture behaviour of polycrystalline silicon carbide. Li et al. [209] studied the effect of porosity on intergranular brittle fractures. In another study, Li et al. [210] performed a thermomechanical analysis of polycrystalline materials. Zhu et al. [211] developed a peridynamic model for fracture analysis of polycrystalline BCC-Fe. Premchander et al. [212] simulated crack propagation in photovoltaic panels by considering a polycrystalline microstructure.
Some materials, such as metals, rocks, or ice, may contain porosity in their microstructure, which should be considered in structural analysis. The effect of porosity should be reflected in the peridynamic model if it is not explicitly modelled. Chen et al. [213] developed a peridynamic model for porous materials suitable to predict brittle fracture. Shen et al. [214] simulated the fracture behaviour of random porous materials. Ni et al. [215] investigated how fracture occurs in dry and saturated porous media. Ozdemir et al. [216] studied the dynamic behaviour of porous media with microcracks. Shangkun et al. [217] performed a fracture simulation of porous material by coupling dual-variable-horizon peridynamics and classical continuum mechanics. Gu et al. [218] predicted the mechanical properties of porous quasi-brittle materials by using peridynamics. Altay et al. [219] examined the dynamic crack behaviour of porous materials based on dual horizon peridynamics.
Peridynamics is also a suitable technique for modelling porous flow. Various studies utilised this new feature of peridynamics. Amongst these, Yan et al. [220] simulated coupled chemical transport and water flow in unsaturated porous media in a peridynamic framework. Katiyar et al. [221] developed a peridynamic model for multiphase transport of non-Newtonian compressible fluids in porous media. Sun and Fish [222] coupled finite element methods and non-ordinary state-based peridynamics to simulate crack propagation in saturated porous media. Ni et al. [223] also introduced a coupled finite element and peridynamic model for saturated porous solids.
Peridynamic simulations can be computationally demanding, especially for three-dimensional models. Therefore, it is important to develop a reduced-order model to accelerate peridynamic simulations, especially for real-time monitoring purposes. Galadima et al. [224] presented a two-dimensional implementation of the coarsening method for linear peridynamics. In another study [225], the authors presented a way to use model order reduction for linear peridynamic systems based on static condensation. They also developed a procedure for static condensation of the peridynamic heat conduction model [226]. Dong et al. [227] introduced an adaptive partitioned reduced-order model of peridynamics. Zhao et al. [228] developed a reduced-order peridynamic model to predict nonlocal heat conduction in nanocomposites.
Stress intensity factor (SIF) is an important parameter in fracture mechanics. It describes the stress field around the crack tip and can be used to determine if the crack has the potential to propagate. There are numerous studies in the literature that provide SIF values for different configurations corresponding to different geometries, loadings, boundary conditions, and material systems. Analytical and numerical approaches such as the finite element method have been widely utilised. SIFs can also be determined by using peridynamics. Dai et al. [229] provided SIFs for mixed-mode conditions for flat shells subjected to in-plane loading conditions. Zhu and Oterkus [230] presented how the displacement extrapolation method can be used to obtain SIFs in the peridynamic framework. Le [231] determined SIFs for mode-I conditions based on tensile stresses and using the virial theorem. Wang et al. [232] calculated SIFs for thermal loading conditions by utilising the domain integral method.
Many structures are operating in harsh conditions, which can cause damage such as fatigue and corrosion. It is critical to take action before any catastrophic situation occurs. Structural health monitoring (SHM) is an effective approach for this purpose, and peridynamics can be used as part of an SHM framework. Kefal et al. [233] demonstrated how to couple peridynamics and inverse finite element method (iFEM) to monitor crack propagation in plate structures.
Deformation behaviour may show non-classical behaviour at small scales due to molecular interactions and surface effects. As a nonlocal approach, peridynamics can be suitable to capture these non-classical behaviours if continuum mechanics can be applied. For instance, Oterkus and Oterkus [234] developed a new peridynamic surface elasticity formulation based on a modified core-shell model.
Although it was originally developed for the mechanical analysis of structures and materials, peridynamics can also be a very effective tool for modelling other fields such as thermal diffusion. A coupled field peridynamic analysis framework can be established by including damage prediction capability. Javili et al. [235] worked on thermomechanical analysis by utilising continuum kinematics–inspired peridynamics. Pathrikar et al. [236] investigated damage occurrence in brittle materials due to the effect of temperature. Wang et al. [237] developed a dual-horizon peridynamic formulation suitable for thermal diffusion analysis. Chen et al. [238] used a fully coupled peridynamic thermomechanical formulation to investigate cracking in concrete. Martowicz et al. [239] investigated phase transformation in shape-memory alloys by performing peridynamic thermomechanical analysis. Wang et al. [240] introduced a thermomechanical phase-change peridynamic model suitable for welding analysis. Liu et al. [241] studied fractures in nuclear fuel pellets based on state-based peridynamic thermomechanical analysis. Zhang et al. [242] applied a fully coupled peridynamic thermomechanical formulation for the analysis of the cracking of frozen rocks. Sun et al. [243] presented a three-dimensional coupled thermomechanical peridynamic model for the fracture analysis of homogeneous and heterogeneous materials. Nikolaev et al. [244] performed peridynamic analysis to investigate the thermal behaviour of phase change material composites for heat storage. Wen et al. [245] developed a peridynamic model for non-Fourier heat transfer in an orthotropic plate with uninsulated cracks. Abdoh [246] introduced a highly efficient algorithm for peridynamic modelling of transient heat conduction in solids.
Computational modelling can be very beneficial in determining the optimum shape of structures under different types of loading conditions. Kefal et al. [247] utilised peridynamics for topology optimisation of structures with cracks. Oh et al. [248] performed shape design optimisation of dynamic crack growth in a peridynamic framework.
Peridynamics is not limited to elastic material behaviour; it can be used for the analysis of other types of material behaviour such as viscoelasticity. Silling [249] investigated the attenuation of waves in a viscoelastic peridynamic medium. Behera et al. [250] studied bonded-lap joints having viscoelastic adhesives by considering finite deformation. Yu and Chen [251] introduced a viscoelastic micropolar peridynamic model suitable for quasi-brittle materials. Ozdemir et al. [252] simulated fracture in viscoelastic membranes. Huang et al. [253] developed a peridynamic model for visco-hyperelastic material behaviour. Tian and Zhou [254] presented a viscoelastic material model in a non-ordinary state-based peridynamic framework. Azizi et al. [255] analysed viscoelastic creep behaviour in a peridynamic framework. Galadima et al. [256] presented a non-ordinary state-based peridynamic formulation suitable for viscoelastic materials.
Due to the nonlocal behaviour of peridynamics, it can represent wave dispersion behaviour differently than classical continuum mechanics. Peridynamic dispersion relationships can be nonlinear as opposed to the linear behaviour of classical continuum mechanics. Zhang et al. [257] presented wave dispersion and propagation in linear peridynamic media. Wang et al. [258] provided analytical wave dispersion relationships for a bond-based peridynamic formulation. Li et al. [259] considered different attenuation functions to investigate wave dispersion in bond-based peridynamics. Oterkus and Oterkus [260] compared wave dispersion relationships obtained from peridynamics and lattice dynamics. Alebrahim et al. [261] compared exact and numerical wave dispersion in peridynamics. Wang et al. [262] presented closed-form wave dispersion relationships in ordinary state-based peridynamics.
In this review study, recent advances in peridynamics research were presented by considering a large number of journal papers. It can be clearly seen that there has been significant progress in peridynamics research during the recent five-year period. In addition to the fundamental developments in peridynamic theory, this formulation has been applied to the analysis of many challenging problems. Some future directions can include artificial intelligence and machine learning, micropolar elasticity, nanomechanics, peridynamic differential operator, soft materials, and surface elasticity.
The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.
This material is based upon work supported by the Air Force Office of Scientific Research under award number FA8655-23-1-7037.
All authors contributed to study conception and design, data collection, analysis and interpretation of results, and manuscript preparation.
Erkan Oterkus and Selda Oterkus are on a special issue editorial board for AIMS Materials Science and were not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.
| [1] |
Javili A, Morasata R, Oterkus E, et al. (2019) Peridynamics review. Math Mech Solids 24: 3714–3739. https://doi.org/10.1177/1081286518803411 doi: 10.1177/1081286518803411
|
| [2] | Oterkus E (2022) Science of cracks: Fracture mechanics. IES J Eng 161: 38–44. |
| [3] |
Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48: 175–209. https://doi.org/10.1016/S0022-5096(99)00029-0 doi: 10.1016/S0022-5096(99)00029-0
|
| [4] | Madenci E, Oterkus E (2013) Peridynamic Theory and its Applications, New York: Springer. https://doi.org/10.1007/978-1-4614-8465-3 |
| [5] |
Hartmann P, Weiß enfels C, Wriggers P (2021) A curing model for the numerical simulation within additive manufacturing of soft polymers using peridynamics. Comp Part Mech 8: 369–388. https://doi.org/10.1007/s40571-020-00337-2 doi: 10.1007/s40571-020-00337-2
|
| [6] |
Karpenko O, Oterkus S, Oterkus E (2021) Peridynamic investigation of the effect of porosity on fatigue nucleation for additively manufactured titanium alloy Ti6Al4V. Theor Appl Fract Mec 112: 102925. https://doi.org/10.1016/j.tafmec.2021.102925 doi: 10.1016/j.tafmec.2021.102925
|
| [7] |
Karpenko O, Oterkus S, Oterkus E (2022) Peridynamic analysis to investigate the influence of microstructure and porosity on fatigue crack propagation in additively manufactured Ti6Al4V. Eng Fract Mech 261: 108212. https://doi.org/10.1016/j.engfracmech.2021.108212 doi: 10.1016/j.engfracmech.2021.108212
|
| [8] |
Karpenko O, Oterkus S, Oterkus E (2022) Investigating the influence of residual stresses on fatigue crack growth for additively manufactured titanium alloy Ti6Al4V by using peridynamics. Int J Fatigue 155: 106624. https://doi.org/10.1016/j.ijfatigue.2021.106624 doi: 10.1016/j.ijfatigue.2021.106624
|
| [9] |
Kendibilir A, Kefal A, Sohouli A, et al. (2022) Peridynamics topology optimtion of three-dimensional structures with surface cracks for additive manufacturing. Comput Method Appl M 401: 115665. https://doi.org/10.1016/j.cma.2022.115665 doi: 10.1016/j.cma.2022.115665
|
| [10] |
Zhu J, Ren X, Cervera M (2023) Peridynamic buildability analysis of 3D-printed concrete including damage, plastic flow and collapse. Addit Manuf 73: 103683. https://doi.org/10.1016/j.addma.2023.103683 doi: 10.1016/j.addma.2023.103683
|
| [11] |
Yang Z, Ma CC, Oterkus E, et al. (2023) Analytical solution of 1-dimensional peridynamic equation of motion. J Peridyn Nonlocal Model 5: 356–374. https://doi.org/10.1007/s42102-022-00086-1 doi: 10.1007/s42102-022-00086-1
|
| [12] |
Yang Z, Ma CC, Oterkus E, et al. (2023) Analytical solution of the peridynamic equation of motion for a 2-dimensional membrane. J Peridyn Nonlocal Model 5: 375–391. https://doi.org/10.1007/s42102-022-00090-5 doi: 10.1007/s42102-022-00090-5
|
| [13] |
Yang Z, Naumenko K, Altenbach H, et al. (2022) Some analytical solutions to peridynamic beam equations. Z Angew Math Mech 102: e202200132. https://doi.org/10.1002/zamm.202200132 doi: 10.1002/zamm.202200132
|
| [14] |
Yang Z, Naumenko K, Ma CC, et al. (2022) Some closed form series solutions to peridynamic plate equations. Mec Res Commun 126: 104000. https://doi.org/10.1016/j.mechrescom.2022.104000 doi: 10.1016/j.mechrescom.2022.104000
|
| [15] |
Mikata Y (2019) Linear peridynamics for isotropic and anisotropic materials. Int J Solids Struct 158: 116–127. https://doi.org/10.1016/j.ijsolstr.2018.09.004 doi: 10.1016/j.ijsolstr.2018.09.004
|
| [16] |
Mikata Y (2023) Analytical solutions of peristatics and peridynamics for 3D isotropic materials. Eur J Mech A-Solid 101: 104978. https://doi.org/10.1016/j.euromechsol.2023.104978 doi: 10.1016/j.euromechsol.2023.104978
|
| [17] |
Kim M, Winovich N, Lin G, et al. (2019) Peri-net: Analysis of crack patterns using deep neural networks. J Peridyn Nonlocal Model 1: 131–142. https://doi.org/10.1007/s42102-019-00013-x doi: 10.1007/s42102-019-00013-x
|
| [18] |
Nguyen CT, Oterkus S, Oterkus E (2020) A peridynamic-based machine learning model for one-dimensional and two-dimensional structures. Continuum Mech Therm 35: 741–773. https://doi.org/10.1007/s00161-020-00905-0 doi: 10.1007/s00161-020-00905-0
|
| [19] |
Nguyen CT, Oterkus S, Oterkus E (2021) A physics-guided machine learning model for two-dimensional structures based on ordinary state-based peridynamics. Theor Appl Fract Mec 112: 102872. https://doi.org/10.1016/j.tafmec.2020.102872 doi: 10.1016/j.tafmec.2020.102872
|
| [20] |
Bekar AC, Madenci E (2021) Peridynamics enabled learning partial differential equations. J Comput Phys 434: 110193. https://doi.org/10.1016/j.jcp.2021.110193 doi: 10.1016/j.jcp.2021.110193
|
| [21] |
Xu X, D'Elia M, Foster JT (2021) A machine-learning framework for peridynamic material models with physical constraints. Comput Method Appl M 386: 114062. https://doi.org/10.1016/j.cma.2021.114062 doi: 10.1016/j.cma.2021.114062
|
| [22] |
Ning L, Cai Z, Dong H, et al. (2023) A peridynamic-informed neural network for continuum elastic displacement characterization. Comput Method Appl M 407: 115909. https://doi.org/10.1016/j.cma.2023.115909 doi: 10.1016/j.cma.2023.115909
|
| [23] |
Babu JR, Gopalakrishanan S (2024) Thermal diffusion in discontinuous media: A hybrid peridynamics-based machine learning model. Comput Struct 290: 107179. https://doi.org/10.1016/j.compstruc.2023.107179 doi: 10.1016/j.compstruc.2023.107179
|
| [24] |
Nguyen CT, Oterkus S (2019) Peridynamics formulation for beam structures to predict damage in offshore structures. Ocean Eng 173: 244–267. https://doi.org/10.1016/j.oceaneng.2018.12.047 doi: 10.1016/j.oceaneng.2018.12.047
|
| [25] |
Nguyen CT, Oterkus S (2019) Peridynamics for the thermomechanical behavior of shell structures. Eng Fract Mech 219: 106623. https://doi.org/10.1016/j.engfracmech.2019.106623 doi: 10.1016/j.engfracmech.2019.106623
|
| [26] |
Diyaroglu C, Oterkus E, Oterkus S (2019) An euler-bernoulli beam formulation in ordinary-state based peridynamic framework. Math Mech Solids 24: 361–376. https://doi.org/10.1177/1081286517728424 doi: 10.1177/1081286517728424
|
| [27] |
Yang Z, Oterkus E, Nguyen CT, et al. (2019) Implementation of peridynamic beam and plate formulations in finite element framework. Continuum Mech Therm 31: 301–315. https://doi.org/10.1007/s00161-018-0684-0 doi: 10.1007/s00161-018-0684-0
|
| [28] |
Yang Z, Oterkus S, Oterkus E (2020) Peridynamic formulation for timoshenko beam. Procedia Struct Integr 28: 464–471. https://doi.org/10.1016/j.prostr.2020.10.055 doi: 10.1016/j.prostr.2020.10.055
|
| [29] |
Yang Z, Vazic B, Diyaroglu C, et al. (2020) A kirchhoff plate formulation in a state-based peridynamic framework. Math Mech Solids 25: 727–738. https://doi.org/10.1177/1081286519887523 doi: 10.1177/1081286519887523
|
| [30] |
Vazic B, Oterkus E, Oterkus S (2020) Peridynamic model for a Mindlin plate resting on a Winkler elastic foundation. J Peridyn Nonlocal Model 2: 229–242. https://doi.org/10.1007/s42102-019-00019-5 doi: 10.1007/s42102-019-00019-5
|
| [31] |
Oterkus E, Madenci E, Oterkus S (2020) Peridynamic shell membrane formulation. Procedia Struct Integr 28: 411–417. https://doi.org/10.1016/j.prostr.2020.10.048 doi: 10.1016/j.prostr.2020.10.048
|
| [32] |
Yolum U, Güler MA (2020) On the peridynamic formulation for an orthotropic Mindlin plate under bending. Math Mech Solids 25: 263–287. https://doi.org/10.1177/1081286519873694 doi: 10.1177/1081286519873694
|
| [33] |
Nguyen CT, Oterkus S (2021) Peridynamics for geometrically nonlinear analysis of three-dimensional beam structures. Eng Anal Bound Elem 126: 68–92. https://doi.org/10.1016/j.enganabound.2021.02.010 doi: 10.1016/j.enganabound.2021.02.010
|
| [34] |
Nguyen CT, Oterkus S (2021) Ordinary state-based peridynamics for geometrically nonlinear analysis of plates. Theor Appl Fract Mec 112: 102877. https://doi.org/10.1016/j.tafmec.2020.102877 doi: 10.1016/j.tafmec.2020.102877
|
| [35] |
Shen G, Xia Y, Li W, et al. (2021) Modeling of peridynamic beams and shells with transverse shear effect via interpolation method. Comput Method Appl M 378: 113716. https://doi.org/10.1016/j.cma.2021.113716 doi: 10.1016/j.cma.2021.113716
|
| [36] |
Yang Z, Oterkus E, Oterkus S (2021) A novel peridynamic mindlin plate formulation without limitation on material constants. J Peridyn Nonlocal Model 3: 287–306. https://doi.org/10.1007/s42102-021-00050-5 doi: 10.1007/s42102-021-00050-5
|
| [37] |
Yang Z, Oterkus E, Oterkus S (2021) Peridynamic higher-order beam formulation. J Peridyn Nonlocal Model 3: 67–83. https://doi.org/10.1007/s42102-020-00043-w doi: 10.1007/s42102-020-00043-w
|
| [38] |
Yang Z, Oterkus E, Oterkus S (2021) Peridynamic formulation for higher-order plate theory. J Peridyn Nonlocal Model 3: 185–210. https://doi.org/10.1007/s42102-020-00047-6 doi: 10.1007/s42102-020-00047-6
|
| [39] |
Zhang Q, Li S, Zhang AM, et al. (2021) A peridynamic Reissner-Mindlin shell theory. Int J Numer Meth Eng 122: 122–147. https://doi.org/10.1002/nme.6527 doi: 10.1002/nme.6527
|
| [40] |
Dai MJ, Tanaka S, Bui TQ, et al. (2021) Fracture parameter analysis of flat shells under out-of-plane loading using ordinary state-based peridynamics. Eng Fract Mech 244: 107560. https://doi.org/10.1016/j.engfracmech.2021.107560 doi: 10.1016/j.engfracmech.2021.107560
|
| [41] |
Dai MJ, Tanaka S, Guan PC, et al. (2021) A peridynamic shell model in arbitrary horizon domains for fracture mechanics analysis. Theor Appl Fract Mec 115: 103068. https://doi.org/10.1016/j.tafmec.2021.103068 doi: 10.1016/j.tafmec.2021.103068
|
| [42] |
Dai MJ, Tanaka S, Oterkus S, et al. (2022) Static and dynamic mechanical behaviors of cracked mindlin plates in ordinary state-based peridynamic framework. Acta Mech 233: 299–316. https://doi.org/10.1007/s00707-021-03127-w doi: 10.1007/s00707-021-03127-w
|
| [43] |
Naumenko K, Eremeyev VA (2022) A non-linear direct peridynamics plate theory. Compos Struct 279: 114728. https://doi.org/10.1016/j.compstruct.2021.114728 doi: 10.1016/j.compstruct.2021.114728
|
| [44] |
Behzadinasab M, Alaydin M, Trask N, et al. (2022) A general-purpose, inelastic, rotation-free Kirchhoff-Love shell formulation for peridynamics. Comput Method Appl M 389: 114422. https://doi.org/10.1016/j.cma.2021.114422 doi: 10.1016/j.cma.2021.114422
|
| [45] |
Yang Z, Naumenko K, Ma CC, et al. (2023) Peridynamic analysis of curved beams. Eur J Mech A-Solid 101: 105075. https://doi.org/10.1016/j.euromechsol.2023.105075 doi: 10.1016/j.euromechsol.2023.105075
|
| [46] |
Xia Y, Wang H, Zheng G, et al. (2023) Mesh-free discretization of peridynamic shell structures and coupling model with isogeometric analysis. Eng Fract Mech 277: 108997. https://doi.org/10.1016/j.engfracmech.2022.108997 doi: 10.1016/j.engfracmech.2022.108997
|
| [47] |
Heo J, Yang Z, Xia W, et al. (2020) Free vibration analysis of cracked plates using peridynamics. Ships Offshore Struc 15: 220–229. https://doi.org/10.1080/17445302.2020.1834266 doi: 10.1080/17445302.2020.1834266
|
| [48] |
Heo J, Yang Z, Xia W, et al. (2020) Buckling analysis of cracked plates using peridynamics. Ocean Eng 214: 107817. https://doi.org/10.1016/j.oceaneng.2020.107817 doi: 10.1016/j.oceaneng.2020.107817
|
| [49] |
Yang Z, Naumenko K, Altenbach H, et al. (2022) Beam buckling analysis in peridynamic framework. Arch Appl Mech 92: 3503–3514. https://doi.org/10.1007/s00419-022-02245-8 doi: 10.1007/s00419-022-02245-8
|
| [50] |
Zhang Y, Cheng Z, Feng H (2019) Dynamic fracture analysis of functional gradient material coating based on the peridynamic method. Coatings 9: 62. https://doi.org/10.3390/coatings9010062 doi: 10.3390/coatings9010062
|
| [51] |
Guski V, Verestek W, Oterkus E, et al. (2020) Microstructural investigation of plasma sprayed ceramic coatings using peridynamics. J Mech 36: 183–196. https://doi.org/10.1017/jmech.2019.58 doi: 10.1017/jmech.2019.58
|
| [52] |
Vasenkov AV (2021) Multi-physics peridynamic modeling of damage processes in protective coatings. J Peridyn Nonlocal Model 3: 167–183. https://doi.org/10.1007/s42102-020-00046-7 doi: 10.1007/s42102-020-00046-7
|
| [53] |
Wang H, Dong H, Cai Z, et al. (2022) Peridynamic-based investigation of the cracking behavior of multilayer thermal barrier coatings. Ceram Int 48: 23543–23553. https://doi.org/10.1016/j.ceramint.2022.05.002 doi: 10.1016/j.ceramint.2022.05.002
|
| [54] |
Wen Z, Hou C, Zhao M, et al. (2023) A peridynamic model for coupled thermo-mechanical-oxygenic analysis of C/C composites with SiC coating. Compos Struct 323: 117441. https://doi.org/10.1016/j.compstruct.2023.117441 doi: 10.1016/j.compstruct.2023.117441
|
| [55] |
Rä del M, Willberg C, Krause D (2019) Peridynamic analysis of fibre-matrix debond and matrix failure mechanisms in composites under transverse tensile load by an energy-based damage criterion. Compos Part B-Eng 158: 18–27. https://doi.org/10.1016/j.compositesb.2018.08.084 doi: 10.1016/j.compositesb.2018.08.084
|
| [56] |
Gao Y, Oterkus S (2019) Fully coupled thermomechanical analysis of laminated composites by using ordinary state based peridynamic theory. Compos Struct 207: 397–424. https://doi.org/10.1016/j.compstruct.2018.09.034 doi: 10.1016/j.compstruct.2018.09.034
|
| [57] |
Hu YL, Yu Y, Madenci E (2020) Peridynamic modeling of composite laminates with material coupling and transverse shear deformation. Compos Struct 253: 112760. https://doi.org/10.1016/j.compstruct.2020.112760 doi: 10.1016/j.compstruct.2020.112760
|
| [58] |
Postek E, Sadowski T (2021) Impact model of the Al2O3/ZrO2 composite by peridynamics. Compos Struct 271: 114071. https://doi.org/10.1016/j.compstruct.2021.114071 doi: 10.1016/j.compstruct.2021.114071
|
| [59] |
Basoglu F, Kefal A, Zerin Z, et al. (2022) Peridynamic modeling of toughening enhancement in unidirectional fiber-reinforced composites with micro-cracks. Compos Struct 297: 115950. https://doi.org/10.1016/j.compstruct.2022.115950 doi: 10.1016/j.compstruct.2022.115950
|
| [60] |
Li FS, Gao WC, Liu W, et al. (2023) Coupling of single-layer material point peridynamics and finite element method for analyzing the fracture behavior of composite laminates. Int J Solids Struct 283: 112495. https://doi.org/10.1016/j.ijsolstr.2023.112495 doi: 10.1016/j.ijsolstr.2023.112495
|
| [61] |
Yang Z, Zheng S, Han F, et al. (2023) An efficient peridynamics-based statistical multiscale method for fracture in composite structures. Int J Mech Sci 259: 108611. https://doi.org/10.1016/j.ijmecsci.2023.108611 doi: 10.1016/j.ijmecsci.2023.108611
|
| [62] |
Madenci E, Yaghoobi A, Barut A, et al. (2023) Peridynamics for failure prediction in variable angle tow composites. Arch Appl Mech 93: 93–107. https://doi.org/10.1007/s00419-022-02216-z doi: 10.1007/s00419-022-02216-z
|
| [63] |
Yang X, Gao W, Liu W, et al. (2023) Peridynamics for out-of-plane damage analysis of composite laminates. Eng Comput. https://doi.org/10.1007/s00366-023-01903-x doi: 10.1007/s00366-023-01903-x
|
| [64] |
Ma Q, Huang D, Wu L, et al. (2023) An extended peridynamic model for analyzing interfacial failure of composite materials with non-uniform discretization. Theor Appl Fract Mec 125: 103854. https://doi.org/10.1016/j.tafmec.2023.103854 doi: 10.1016/j.tafmec.2023.103854
|
| [65] |
Wang H, Tanaka S, Oterkus S, et al. (2024) Fracture mechanics investigation for 2D orthotropic materials by using ordinary state-based peridynamics. Compos Struct 329: 117757. https://doi.org/10.1016/j.compstruct.2023.117757 doi: 10.1016/j.compstruct.2023.117757
|
| [66] |
Kamensky D, Behzadinasab M, Foster JT, et al. (2019) Peridynamic modeling of frictional contact. J Peridyn Nonlocal Model 1: 107–121. https://doi.org/10.1007/s42102-019-00012-y doi: 10.1007/s42102-019-00012-y
|
| [67] |
Lu W, Oterkus S, Oterkus E (2020) Peridynamic modelling of hertzian indentation fracture. Procedia Struct Integr 28: 1559–1571. https://doi.org/10.1016/j.prostr.2020.10.128 doi: 10.1016/j.prostr.2020.10.128
|
| [68] |
Lu W, Oterkus S, Oterkus E, et al. (2021) Modelling of cracks with frictional contact based on peridynamics. Theor Appl Fract Mec 116: 103082. https://doi.org/10.1016/j.tafmec.2021.103082 doi: 10.1016/j.tafmec.2021.103082
|
| [69] |
Wang L, Sheng X, Luo J (2022) A peridynamic frictional contact model for contact fatigue crack initiation and propagation. Eng Fract Mech 264: 108338. https://doi.org/10.1016/j.engfracmech.2022.108338 doi: 10.1016/j.engfracmech.2022.108338
|
| [70] |
Zhang H, Zhang X, Liu Y (2022) A peridynamic model for contact problems involving fracture. Eng Fract Mech 267: 108436. https://doi.org/10.1016/j.engfracmech.2022.108436 doi: 10.1016/j.engfracmech.2022.108436
|
| [71] |
Mohajerani S, Wang G (2022) "Touch–aware" contact model for peridynamics modeling of granular systems. Int J Numer Meth Eng 123: 3850–3878. https://doi.org/10.1002/nme.7000 doi: 10.1002/nme.7000
|
| [72] |
Guan J, Yan X, Guo L (2023) An adaptive contact model involving friction based on peridynamics. Eur J Mech A-Solid 100: 104966. https://doi.org/10.1016/j.euromechsol.2023.104966 doi: 10.1016/j.euromechsol.2023.104966
|
| [73] |
Zhu F, Zhao JD, Ballarini R, et al. (2022) Peridynamic modeling of stochastic fractures in bolted glass plates. Mech Res Commun 122: 103890. https://doi.org/10.1016/j.mechrescom.2022.103890 doi: 10.1016/j.mechrescom.2022.103890
|
| [74] |
Naumenko K, Pander M, Würkner M (2022) Damage patterns in float glass plates: Experiments and peridynamics analysis. Theor Appl Fract Mec 118: 103264. https://doi.org/10.1016/j.tafmec.2022.103264 doi: 10.1016/j.tafmec.2022.103264
|
| [75] |
Rokkam S, Gunzburger M, Brothers M, et al. (2019) A nonlocal peridynamics modeling approach for corrosion damage and crack propagation. Theor Appl Fract Mec 101: 373–387. https://doi.org/10.1016/j.tafmec.2019.03.010 doi: 10.1016/j.tafmec.2019.03.010
|
| [76] |
Nguyen CT, Oterkus S (2021) Brittle damage prediction for corroded stiffened structures under static loading conditions by using peridynamics. Ships Offshore Struc 16: 153–170. https://doi.org/10.1080/17445302.2021.1884811 doi: 10.1080/17445302.2021.1884811
|
| [77] |
Karpenko O, Oterkus S, Oterkus E (2022) Titanium alloy corrosion fatigue crack growth rates prediction: Peridynamics based numerical approach. Int J Fatigue 162: 107023. https://doi.org/10.1016/j.ijfatigue.2022.107023 doi: 10.1016/j.ijfatigue.2022.107023
|
| [78] |
Jafarzadeh S, Zhao J, Shakouri M, et al. (2022) A peridynamic model for crevice corrosion damage. Electrochim Acta 401: 139512. https://doi.org/10.1016/j.electacta.2021.139512 doi: 10.1016/j.electacta.2021.139512
|
| [79] |
Tan C, Qian S, Zhang J (2022) Crack extension analysis of atmospheric stress corrosion based on peridynamics. Appl Sci 12: 10008. https://doi.org/10.3390/app121910008 doi: 10.3390/app121910008
|
| [80] |
Wang H, Dong H, Cai Z, et al. (2023) Corrosion fatigue crack growth in stainless steels: A peridynamic study. Int J Mech Sci 254: 108445. https://doi.org/10.1016/j.ijmecsci.2023.108445 doi: 10.1016/j.ijmecsci.2023.108445
|
| [81] |
Zhou XP, Du EB, Wang YT (2023) Chemo-mechanical coupling bond-based peridynamic model for electrochemical corrosion and stress chemical corrosion. Eng Anal Bound Elem 151: 360–369. https://doi.org/10.1016/j.enganabound.2023.03.013 doi: 10.1016/j.enganabound.2023.03.013
|
| [82] |
Basoglu MF, Zerin Z, Kefal A, et al. (2019) Peridynamic model for deflecting propagation of cracks with micro-cracks. Comp Mater Sci 162: 33–46. https://doi.org/10.1016/j.commatsci.2019.02.032 doi: 10.1016/j.commatsci.2019.02.032
|
| [83] |
Karpenko O, Oterkus S, Oterkus E (2020) Influence of different types of small-size defects on propagation of macro-cracks in brittle materials. J Peridyn Nonlocal Model 2: 289–316. https://doi.org/10.1007/s42102-020-00032-z doi: 10.1007/s42102-020-00032-z
|
| [84] |
Rahimi N, Kefal A, Yildiz M, et al. (2020) An ordinary state-based peridynamic model for toughness enhancement of brittle materials through drilling stop-holes. Int J Mech Sci 182: 105773. https://doi.org/10.1016/j.ijmecsci.2020.105773 doi: 10.1016/j.ijmecsci.2020.105773
|
| [85] |
Candas A, Oterkus E, Irmak CE (2021) Dynamic crack propagation and its interaction with micro-cracks in an impact problem. J Eng Mater-T ASME 143: 011003. https://doi.org/10.1115/1.4047746 doi: 10.1115/1.4047746
|
| [86] |
Wang J, Yu Y, Mu Z, et al. (2022) Peridynamic meso-scale modeling for degradation in transverse mechanical properties of composites with micro-void defects. Acta Mech Solida Sin 35: 813–823. https://doi.org/10.1007/s10338-022-00329-0 doi: 10.1007/s10338-022-00329-0
|
| [87] |
Ozdemir M, Imachi M, Tanaka S, et al. (2022) A comprehensive investigation on macro-micro crack interactions in functionally graded materials using ordinary-state based peridynamics. Compos Struct 287: 115299. https://doi.org/10.1016/j.compstruct.2022.115299 doi: 10.1016/j.compstruct.2022.115299
|
| [88] |
Cheng Z, Wang Z, Luo Z (2019) Dynamic fracture analysis for shale material by peridynamic modelling. CMES-Comp Model Eng 118: 509–527. https://doi.org/10.31614/cmes.2019.04339 doi: 10.31614/cmes.2019.04339
|
| [89] |
Imachi M, Tanaka S, Ozdemir M, et al. (2020) Dynamic crack arrest analysis by ordinary state-based peridynamics. Int J Fracture 221: 155–169. https://doi.org/10.1007/s10704-019-00416-3 doi: 10.1007/s10704-019-00416-3
|
| [90] |
Butt SN, Meschke G (2021) Peridynamic analysis of dynamic fracture: influence of peridynamic horizon, dimensionality and specimen size. Comput Mech 67: 1719–1745. https://doi.org/10.1007/s00466-021-02017-1 doi: 10.1007/s00466-021-02017-1
|
| [91] |
Yang Y, Liu Y (2022) Analysis of dynamic crack propagation in two-dimensional elastic bodies by coupling the boundary element method and the bond-based peridynamics. Comput Method Appl M 399: 115339. https://doi.org/10.1016/j.cma.2022.115339 doi: 10.1016/j.cma.2022.115339
|
| [92] |
Imachi M, Tanaka S, Bui TQ, et al. (2019) A computational approach based on ordinary state-based peridynamics with new transition bond for dynamic fracture analysis. Eng Fract Mech 206: 359–374. https://doi.org/10.1016/j.engfracmech.2018.11.054 doi: 10.1016/j.engfracmech.2018.11.054
|
| [93] |
Jiang XW, Wang H, Guo S (2019) Peridynamic open-hole tensile strength prediction of fiber-reinforced composite laminate using energy-based failure criteria. Adv Mater Sci Eng 2019: 7694081. https://doi.org/10.1155/2019/7694081 doi: 10.1155/2019/7694081
|
| [94] |
Karpenko O, Oterkus S, Oterkus E (2020) An in-depth investigation of critical stretch based failure criterion in ordinary state-based peridynamics. Int J Fracture 226: 97–119. https://doi.org/10.1007/s10704-020-00481-z doi: 10.1007/s10704-020-00481-z
|
| [95] |
Silling SA (2021) Kinetics of failure in an elastic peridynamic material. J Peridyn Nonlocal Model 3: 1–23. https://doi.org/10.1007/s42102-020-00031-0 doi: 10.1007/s42102-020-00031-0
|
| [96] |
Wang Y, Han F, Lubineau G (2021) Strength-induced peridynamic modeling and simulation of fractures in brittle materials. Comput Method Appl M 374: 113558. https://doi.org/10.1016/j.cma.2020.113558 doi: 10.1016/j.cma.2020.113558
|
| [97] |
Kumagai T (2021) A parameter to represent a local deformation mode and a fracture criterion based on the parameter in ordinary-state based peridynamics. Int J Solids Struct 217: 40–47. https://doi.org/10.1016/j.ijsolstr.2021.01.025 doi: 10.1016/j.ijsolstr.2021.01.025
|
| [98] |
Ignatiev MO, Petrov YV, Kazarinov NA, et al. (2023) Peridynamic formulation of the mean stress and incubation time fracture criteria and its correspondence to the classical griffith's approach. Continuum Mech Therm 35: 1523–1534. https://doi.org/10.1007/s00161-022-01159-8 doi: 10.1007/s00161-022-01159-8
|
| [99] |
Ma X, Xu J, Liu L, et al. (2020) A 2D peridynamic model for fatigue crack initiation of railheads. Int J Fatigue 135: 105536. https://doi.org/10.1016/j.ijfatigue.2020.105536 doi: 10.1016/j.ijfatigue.2020.105536
|
| [100] |
Han J, Chen W (2020) An ordinary state-based peridynamic model for fatigue cracking of ferrite and pearlite wheel material. Appl Sci 10: 4325. https://doi.org/10.3390/app10124325 doi: 10.3390/app10124325
|
| [101] |
Nguyen CT, Oterkus S, Oterkus E (2021) Peridynamic model for predicting fatigue crack growth under overload and underload. Theor Appl Fract Mec 116: 103115. https://doi.org/10.1016/j.tafmec.2021.103115 doi: 10.1016/j.tafmec.2021.103115
|
| [102] |
Hong K, Oterkus S, Oterkus E (2021) Peridynamic analysis of fatigue crack growth in fillet welded joints. Ocean Eng 235: 109348. https://doi.org/10.1016/j.oceaneng.2021.109348 doi: 10.1016/j.oceaneng.2021.109348
|
| [103] |
Bang DJ, Ince A, Oterkus E, et al. (2021) Crack growth modeling and simulation of a peridynamic fatigue model based on numerical and analytical solution approaches. Theor Appl Fract Mec 114: 103026. https://doi.org/10.1016/j.tafmec.2021.103026 doi: 10.1016/j.tafmec.2021.103026
|
| [104] |
Zhu N, Kochan C, Oterkus E, et al. (2021) Fatigue analysis of polycrystalline materials using peridynamic theory with a novel crack tip detection algorithm. Ocean Eng 222: 108572. https://doi.org/10.1016/j.oceaneng.2021.108572 doi: 10.1016/j.oceaneng.2021.108572
|
| [105] |
Nguyen CT, Oterkus S, Oterkus E (2021) An energy-based peridynamic model for fatigue cracking. Eng Fract Mech 241: 107373. https://doi.org/10.1016/j.engfracmech.2020.107373 doi: 10.1016/j.engfracmech.2020.107373
|
| [106] |
Liu B, Bao R, Sui F (2021) A fatigue damage-cumulative model in peridynamics. Chinese J Aeronaut 34: 329–342. https://doi.org/10.1016/j.cja.2020.09.046 doi: 10.1016/j.cja.2020.09.046
|
| [107] |
Li H, Hao Z, Li P, et al. (2022) A low cycle fatigue cracking simulation method of non-ordinary state-based peridynamics. Int J Fatigue 156: 106638. https://doi.org/10.1016/j.ijfatigue.2021.106638 doi: 10.1016/j.ijfatigue.2021.106638
|
| [108] |
Hamarat M, Papaelias M, Kaewunruen S (2022) Fatigue damage assessment of complex railway turnout crossings via peridynamics-based digital twin. Sci Rep 12: 14377. https://doi.org/10.1038/s41598-022-18452-w doi: 10.1038/s41598-022-18452-w
|
| [109] |
Zhang Y, Madenci E (2022) A coupled peridynamic and finite element approach in ANSYS framework for fatigue life prediction based on the kinetic theory of fracture. J Peridyn Nonlocal Model 4: 51–87. https://doi.org/10.1007/s42102-021-00055-0 doi: 10.1007/s42102-021-00055-0
|
| [110] |
Cao X, Qin X, Li H, et al. (2022) Non-ordinary state-based peridynamic fatigue modelling of composite laminates with arbitrary fibre orientation. Theor Appl Fract Mec 120: 103393. https://doi.org/10.1016/j.tafmec.2022.103393 doi: 10.1016/j.tafmec.2022.103393
|
| [111] |
Cruz AL, Donadon MV (2022) A mixed-mode energy-based elastoplastic fatigue induced damage model for the peridynamic theory. Eng Fract Mech 275: 108834. https://doi.org/10.1016/j.engfracmech.2022.108834 doi: 10.1016/j.engfracmech.2022.108834
|
| [112] |
Bang DJ, Ince A (2022) Integration of a peridynamic fatigue model with two-parameter crack driving force. Eng Comput 38: 2859–2877. https://doi.org/10.1007/s00366-022-01619-4 doi: 10.1007/s00366-022-01619-4
|
| [113] |
Nguyen CT, Oterkus S, Oterkus E, et al. (2023) Fatigue crack prediction in ceramic material and its porous media by using peridynamics. Procedia Struct Integr 46: 80–86. https://doi.org/10.1016/j.prostr.2023.06.014 doi: 10.1016/j.prostr.2023.06.014
|
| [114] |
Wang H, Tanaka S, Oterkus S, et al. (2023) Study on two-dimensional mixed-mode fatigue crack growth employing ordinary state-based peridynamics. Theor Appl Fract Mec 124: 103761. https://doi.org/10.1016/j.tafmec.2023.103761 doi: 10.1016/j.tafmec.2023.103761
|
| [115] |
Ni T, Zaccariotto M, Galvanetto U (2023) A peridynamic approach to simulating fatigue crack propagation in composite materials. Philos T R Soc A 381: 20210217. https://doi.org/10.1098/rsta.2021.0217 doi: 10.1098/rsta.2021.0217
|
| [116] |
Altay U, Dorduncu M, Kadioglu S (2023) An improved peridynamic approach for fatigue analysis of two dimensional functionally graded materials. Theor Appl Fract Mec 128: 104152. https://doi.org/10.1016/j.tafmec.2023.104152 doi: 10.1016/j.tafmec.2023.104152
|
| [117] |
Chen Y, Yang Y, Liu Y (2023) Fatigue crack growth analysis of hydrogel by using peridynamics. Int J Fract 244: 113–123. https://doi.org/10.1007/s10704-023-00722-x doi: 10.1007/s10704-023-00722-x
|
| [118] |
Cheng Z, Jia X, Tang J, et al. (2023) Peridynamic study of fatigue failure of engineered cementitious composites. Eng Fract Mech 293: 109704. https://doi.org/10.1016/j.engfracmech.2023.109704 doi: 10.1016/j.engfracmech.2023.109704
|
| [119] |
Zhang Z, Chen Z (2024) A peridynamic model for structural fatigue crack propagation analysis under spectrum loadings. Int J Fatigue 181: 108129. https://doi.org/10.1016/j.ijfatigue.2023.108129 doi: 10.1016/j.ijfatigue.2023.108129
|
| [120] |
Gao Y, Oterkus S (2019) Nonlocal numerical simulation of low Reynolds number laminar fluid motion by using peridynamic differential operator. Ocean Eng 179: 135–158. https://doi.org/10.1016/j.oceaneng.2019.03.035 doi: 10.1016/j.oceaneng.2019.03.035
|
| [121] |
Mikata Y (2021) Peridynamics for fluid mechanics and acoustics. Acta Mech 232: 3011–3032. https://doi.org/10.1007/s00707-021-02947-0 doi: 10.1007/s00707-021-02947-0
|
| [122] |
Nguyen CT, Oterkus S, Oterkus E, et al. (2021) Peridynamic model for incompressible fluids based on eulerian approach. Ocean Eng 239: 109815. https://doi.org/10.1016/j.oceaneng.2021.109815 doi: 10.1016/j.oceaneng.2021.109815
|
| [123] |
Kim KH, Bhalla AP, Griffith BE (2023) An immersed peridynamics model of fluid-structure interaction accounting for material damage and failure. J Comput Phys 493: 112466. https://doi.org/10.1016/j.jcp.2023.112466 doi: 10.1016/j.jcp.2023.112466
|
| [124] | Wang B, Oterkus S, Oterkus E (2023) Nonlocal modelling of multiphase flow wetting and thermo-capillary flow by using peridynamic differential operator. Eng Comput. https://doi.org/10.1007/s00366-023-01888-7 |
| [125] |
Cheng ZQ, Sui ZB, Yin H, et al. (2019) Studies of dynamic fracture in functionally graded materials using peridynamic modeling with composite weighted bond. Theor Appl Fract Mec 103: 102242. https://doi.org/10.1016/j.tafmec.2019.102242 doi: 10.1016/j.tafmec.2019.102242
|
| [126] |
Cheng Z, Sui Z, Yin H, et al. (2019) Numerical simulation of dynamic fracture in functionally graded materials using peridynamic modeling with composite weighted bonds. Eng Anal Bound Elem 105: 31–46. https://doi.org/10.1016/j.enganabound.2019.04.005 doi: 10.1016/j.enganabound.2019.04.005
|
| [127] |
Dorduncu M (2020) Stress analysis of sandwich plates with functionally graded cores using peridynamic differential operator and refined zigzag theory. Thin Wall Struct 146: 106468. https://doi.org/10.1016/j.tws.2019.106468 doi: 10.1016/j.tws.2019.106468
|
| [128] |
Ozdemir M, Kefal A, Imachi M, et al. (2020) Dynamic fracture analysis of functionally graded materials using ordinary state-based peridynamics. Compos Struct 244: 112296. https://doi.org/10.1016/j.compstruct.2020.112296 doi: 10.1016/j.compstruct.2020.112296
|
| [129] |
Yang Z, Oterkus E, Oterkus S (2020) A state-based peridynamic formulation for functionally graded euler-bernoulli beams. CMES-Comp Model Eng 124: 527–544. https://doi.org/10.32604/cmes.2020.010804 doi: 10.32604/cmes.2020.010804
|
| [130] |
Yang Z, Oterkus E, Oterkus S (2020) Peridynamic mindlin plate formulation for functionally graded materials. J Compos Sci 4: 76. https://doi.org/10.3390/jcs4020076 doi: 10.3390/jcs4020076
|
| [131] |
Yang Z, Oterkus E, Oterkus S (2021) Analysis of functionally graded timoshenko beams by using peridynamics. J Peridyn Nonlocal Model 3: 148–166. https://doi.org/10.1007/s42102-020-00044-9 doi: 10.1007/s42102-020-00044-9
|
| [132] |
Yang Z, Oterkus E, Oterkus S (2021) A state-based peridynamic formulation for functionally graded Kirchhoff plates. Math Mech Solids 26: 530–551. https://doi.org/10.1177/1081286520963383 doi: 10.1177/1081286520963383
|
| [133] |
Yang Z, Oterkus E, Oterkus S (2021) Peridynamic formulation for higher order functionally graded beams. Thin Wall Struct 160: 107343. https://doi.org/10.1016/j.tws.2020.107343 doi: 10.1016/j.tws.2020.107343
|
| [134] |
Yang Z, Oterkus E, Oterkus S (2021) Peridynamic modelling of higher order functionally graded plates. Math Mech Solids 26: 1737–1759. https://doi.org/10.1177/10812865211004671 doi: 10.1177/10812865211004671
|
| [135] |
He D, Huang D, Jiang D (2021) Modeling and studies of fracture in functionally graded materials under thermal shock loading using peridynamics. Theor Appl Fract Mec 111: 102852. https://doi.org/10.1016/j.tafmec.2020.102852 doi: 10.1016/j.tafmec.2020.102852
|
| [136] |
Dorduncu M, Olmus I, Rabczuk T (2022) A peridynamic approach for modeling of two dimensional functionally graded plates. Compos Struct 279: 114743. https://doi.org/10.1016/j.compstruct.2021.114743 doi: 10.1016/j.compstruct.2021.114743
|
| [137] |
Wang H, Tanaka S, Oterkus S, et al. (2022) Fracture parameter investigations of functionally graded materials by using ordinary state based peridynamics. Eng Anal Bound Elem 139: 180–191. https://doi.org/10.1016/j.enganabound.2022.03.005 doi: 10.1016/j.enganabound.2022.03.005
|
| [138] |
Candas A, Oterkus E, Imrak CE (2023) Peridynamic simulation of dynamic fracture in functionally graded materials subjected to impact load. Eng Comput 39: 253–267. https://doi.org/10.1007/s00366-021-01540-2 doi: 10.1007/s00366-021-01540-2
|
| [139] | Candas A, Oterkus E, Imrak CE (2023) Ordinary state-based peridynamic modelling of crack propagation in functionally graded materials with micro cracks under impact loading. Mech Adv Mater Struct. https://doi.org/10.1080/15376494.2023.2287180 |
| [140] |
Jiang X, Fang G, Liu S, et al. (2024) Fracture analysis of orthotropic functionally graded materials using element-based peridynamics. Eng Fract Mech 297: 109886. https://doi.org/10.1016/j.engfracmech.2024.109886 doi: 10.1016/j.engfracmech.2024.109886
|
| [141] |
Celik E, Oterkus E, Guven I (2019) Peridynamic simulations of nanoindentation tests to determine elastic modulus of polymer thin films. J Peridyn Nonlocal Model 1: 36–44. https://doi.org/10.1007/s42102-019-0005-4 doi: 10.1007/s42102-019-0005-4
|
| [142] |
Liu X, Bie Z, Wang J, et al. (2019) Investigation on fracture of pre-cracked single-layer graphene sheets. Comp Mater Sci 159: 365–375. https://doi.org/10.1016/j.commatsci.2018.12.014 doi: 10.1016/j.commatsci.2018.12.014
|
| [143] |
Liu X, He X, Sun L, et al. (2020) A chirality-dependent peridynamic model for the fracture analysis of graphene sheets. Mech Mater 149: 103535. https://doi.org/10.1016/j.mechmat.2020.103535 doi: 10.1016/j.mechmat.2020.103535
|
| [144] |
Silling SA, Fermen-Coker M (2021) Peridynamic model for microballistic perforation of multilayer graphene. Theor Appl Fract Mec 113: 102947. https://doi.org/10.1016/j.tafmec.2021.102947 doi: 10.1016/j.tafmec.2021.102947
|
| [145] |
Torkaman-Asadi MA, Kouchakzadeh MA (2023) Fracture analysis of pre-cracked graphene layer sheets using peridynamic theory. Int J Fracture 243: 229–245. https://doi.org/10.1007/s10704-023-00744-5 doi: 10.1007/s10704-023-00744-5
|
| [146] |
Liu X, He X, Oterkus E, et al. (2023) Peridynamic simulation of fracture in polycrystalline graphene. J Peridyn Nonlocal Model 5: 260–274. https://doi.org/10.1007/s42102-021-00073-y doi: 10.1007/s42102-021-00073-y
|
| [147] |
Silling SA, D'Elia M, Yu Y, et al. (2023) Peridynamic model for single-layer graphene obtained from coarse-grained bond forces. J Peridyn Nonlocal Model 5: 183–204. https://doi.org/10.1007/s42102-021-00075-w doi: 10.1007/s42102-021-00075-w
|
| [148] |
Liu X, Yu P, Zheng B, et al. (2024) Prediction of Mechanical and fracture properties of graphene via peridynamics. Int J Mech Sci 266: 108914. https://doi.org/10.1016/j.ijmecsci.2023.108914 doi: 10.1016/j.ijmecsci.2023.108914
|
| [149] |
Liu X, Bie Z, Yu P, et al. (2024) Peridynamics for the fracture study on multi-layer graphene sheets. Compos Struct 332: 117926. https://doi.org/10.1016/j.compstruct.2024.117926 doi: 10.1016/j.compstruct.2024.117926
|
| [150] |
Xia W, Galadima YK, Oterkus E, et al. (2019) Representative volume element homogenisation of a composite material by using bond-based peridynamics. J Compos Biodegrad Polym 7: 51–56. https://doi.org/10.12974/2311-8717.2019.07.7 doi: 10.12974/2311-8717.2019.07.7
|
| [151] |
Diyaroglu C, Madenci E, Phan N (2019) Peridynamic homogenization of microstructures with orthotropic constituents in a finite element framework. Compos Struct 227: 111334. https://doi.org/10.1016/j.compstruct.2019.111334 doi: 10.1016/j.compstruct.2019.111334
|
| [152] |
Buryachenko VA (2019) Computational homogenization in linear elasticity of peristatic periodic structure composites. Math Mech Solids 24: 2497–2525. https://doi.org/10.1177/1081286518768039 doi: 10.1177/1081286518768039
|
| [153] |
Galadima YK, Oterkus E, Oterkus S (2020) Investigation of the effect of shape of inclusions on homogenized properties by using peridynamics. Procedia Struct Integr 28: 1094–1105. https://doi.org/10.1016/j.prostr.2020.11.124 doi: 10.1016/j.prostr.2020.11.124
|
| [154] |
Xia W, Oterkus E, Oterkus S (2020) Peridynamic modelling of periodic microstructured materials. Procedia Struct Integr 28: 820–828. https://doi.org/10.1016/j.prostr.2020.10.096 doi: 10.1016/j.prostr.2020.10.096
|
| [155] |
Eriksson K, Stenströ m C (2021) Homogenization of the 1D peri-static/dynamic bar with triangular micromodulus. J Peridyn Nonlocal Model 3: 85–112. https://doi.org/10.1007/s42102-020-00042-x doi: 10.1007/s42102-020-00042-x
|
| [156] |
Xia W, Oterkus E, Oterkus S (2021) 3-Dimensional bond-based peridynamic representative volume element homogenisation. Phys Mesomech 24: 45–51. https://doi.org/10.1134/S1029959921050052 doi: 10.1134/S1029959921050052
|
| [157] |
Xia W, Oterkus E, Oterkus S (2021) Ordinary state based peridynamic homogenization of periodic micro-structured materials. Theor Appl Fract Mec 113: 102960. https://doi.org/10.1016/j.tafmec.2021.102960 doi: 10.1016/j.tafmec.2021.102960
|
| [158] | Buryachenko VA (2022) Computational homogenization in linear peridynamic micromechanics of periodic structure CMs, In: Buryachenko VA, Local and Nonlocal Micromechanics of Heterogeneous Materials, Cham: Springer, 849–899. https://doi.org/10.1007/978-3-030-81784-8_19 |
| [159] |
Li J, Wang Q, Li X, et al. (2022) Homogenization of periodic microstructure based on representative volume element using improved bond-based peridynamics. Eng Anal Bound Elem 143: 152–162. https://doi.org/10.1016/j.enganabound.2022.06.005 doi: 10.1016/j.enganabound.2022.06.005
|
| [160] |
Galadima YK, Oterkus S, Oterkus E, et al. (2024) Effect of phase contrast and inclusion shape on the effective response of viscoelastic composites using peridynamic computational homogenization theory. Mech Adv Mater Struct 31: 155–163. https://doi.org/10.1080/15376494.2023.2218364 doi: 10.1080/15376494.2023.2218364
|
| [161] |
Galadima YK, Oterkus S, Oterkus E, et al. (2023) A nonlocal method to compute effective properties of viscoelastic composite materials based on peridynamic computational homogenization theory. Compos Struct 319: 117147. https://doi.org/10.1016/j.compstruct.2023.117147 doi: 10.1016/j.compstruct.2023.117147
|
| [162] |
Galadima YK, Xia W, Oterkus E, et al. (2023) Peridynamic computational homogenization theory for materials with evolving microstructure and damage. Eng Comput 39: 2945–2957. https://doi.org/10.1007/s00366-022-01696-5 doi: 10.1007/s00366-022-01696-5
|
| [163] |
Galadima YK, Xia W, Oterkus E, et al. (2023) A computational homogenization framework for non-ordinary state-based peridynamics. Eng Comput 39: 461–487. https://doi.org/10.1007/s00366-021-01582-6 doi: 10.1007/s00366-021-01582-6
|
| [164] |
Buryachenko VA (2024) Generalized Mori-Tanaka approach in peridynamic micromechanics of multilayered composites of random structure. J Peridyn Nonlocal Model: 1–24. https://doi.org/10.1007/s42102-023-00114-8 doi: 10.1007/s42102-023-00114-8
|
| [165] |
Qi J, Li C, Tie Y, et al. (2024) A peridynamic-based homogenization method to compute effective properties of periodic microstructure. Comp Part Mech. https://doi.org/10.1007/s40571-023-00698-4 doi: 10.1007/s40571-023-00698-4
|
| [166] |
Oterkus S, Wang B, Oterkus E (2020) Effect of horizon shape in peridynamics. Procedia Struct Integr 28: 418–429. https://doi.org/10.1016/j.prostr.2020.10.049 doi: 10.1016/j.prostr.2020.10.049
|
| [167] |
Vazic B, Diyaroglu C, Oterkus E, et al. (2020) Family member search algorithms for peridynamic analysis. J Peridyn Nonlocal Model 2: 59–84. https://doi.org/10.1007/s42102-019-00027-5 doi: 10.1007/s42102-019-00027-5
|
| [168] |
Wang B, Oterkus S, Oterkus E (2023) Determination of horizon size in state-based peridynamics. Continuum Mech Therm 35: 705–728. https://doi.org/10.1007/s00161-020-00896-y doi: 10.1007/s00161-020-00896-y
|
| [169] |
Song Y, Yu H, Kang Z (2019) Numerical study on ice fragmentation by impact based on non-ordinary state-based peridynamics. J Micromech Mol Phys 4: 1850006. https://doi.org/10.1142/S2424913018500066 doi: 10.1142/S2424913018500066
|
| [170] |
Ye LY, Guo CY, Wang C, et al. (2020) Peridynamic solution for submarine surfacing through ice. Ships Offshore Struc 15: 535–549. https://doi.org/10.1080/17445302.2019.1661626 doi: 10.1080/17445302.2019.1661626
|
| [171] |
Vazic B, Oterkus E, Oterkus S (2020) In-plane and out-of-plane failure of an ice sheet using peridynamics. J Mech 36: 265–271. https://doi.org/10.1017/jmech.2019.65 doi: 10.1017/jmech.2019.65
|
| [172] |
Liu R, Yan J, Li S (2020) Modeling and simulation of ice–water interactions by coupling peridynamics with updated Lagrangian particle hydrodynamics. Comp Part Mech 7: 241–255. https://doi.org/10.1007/s40571-019-00268-7 doi: 10.1007/s40571-019-00268-7
|
| [173] |
Lu W, Li M, Vazic B, et al. (2020) Peridynamic modelling of fracture in polycrystalline ice. J Mech 36: 223–234. https://doi.org/10.1017/jmech.2019.61 doi: 10.1017/jmech.2019.61
|
| [174] |
Liu R, Xue Y, Han D, et al. (2021) Studies on model-scale ice using micro-potential-based peridynamics. Ocean Eng 221: 108504. https://doi.org/10.1016/j.oceaneng.2020.108504 doi: 10.1016/j.oceaneng.2020.108504
|
| [175] |
Guo CY, Han K, Wang C, et al. (2022) Numerical modelling of the dynamic ice-milling process and structural response of a propeller blade profile with state-based peridynamics. Ocean Eng 264: 112457. https://doi.org/10.1016/j.oceaneng.2022.112457 doi: 10.1016/j.oceaneng.2022.112457
|
| [176] |
Zhang Y, Wang Q, Oterkus S, et al. (2023) Numerical investigation of ice plate fractures upon rigid ball impact. Ocean Eng 287: 115824. https://doi.org/10.1016/j.oceaneng.2023.115824 doi: 10.1016/j.oceaneng.2023.115824
|
| [177] |
Song Y, Li S, Li Y (2023) Peridynamic modeling and simulation of thermo-mechanical fracture in inhomogeneous ice. Eng Comput 39: 575–606. https://doi.org/10.1007/s00366-022-01616-7 doi: 10.1007/s00366-022-01616-7
|
| [178] |
Xiong W, Wang C, Zhang Y, et al. (2023) Numerical simulation of impact process between spherical ice and a rigid plate based on the ordinary state-based peridynamics. Ocean Eng 288: 116191. https://doi.org/10.1016/j.oceaneng.2023.116191 doi: 10.1016/j.oceaneng.2023.116191
|
| [179] |
Zhang Y, Zhang G, Tao L, et al. (2023) Study and discussion on computational efficiency of ice–structure interaction by peridynamic. J Mar Sci Eng 11: 1154. https://doi.org/10.3390/jmse11061154 doi: 10.3390/jmse11061154
|
| [180] |
Rivera J, Berjikian J, Ravinder R, et al. (2019) Glass fracture upon ballistic impact: new insights from peridynamics simulations. Front Mat 6: 239. https://doi.org/10.3389/fmats.2019.00239 doi: 10.3389/fmats.2019.00239
|
| [181] |
Kazemi SR (2020) Plastic deformation due to high-velocity impact using ordinary state-based peridynamic theory. Int J Impact Eng 137: 103470. https://doi.org/10.1016/j.ijimpeng.2019.103470 doi: 10.1016/j.ijimpeng.2019.103470
|
| [182] |
Ha YD (2020) An extended ghost interlayer model in peridynamic theory for high-velocity impact fracture of laminated glass structures. Comput Math Appl 80: 744–761. https://doi.org/10.1016/j.camwa.2020.05.003 doi: 10.1016/j.camwa.2020.05.003
|
| [183] | Altenbach H, Larin O, Naumenko K, et al. (2022) Elastic plate under low velocity impact: Classical continuum mechanics vs peridynamics analysis. AIMS Mater Sci 9: 702–718. 10.3934/matersci.2022043 |
| [184] |
Zheng J, Shen F, Gu X, et al. (2022) Simulating failure behavior of reinforced concrete T-beam under impact loading by using peridynamics. Int J Impact Eng 165: 104231. https://doi.org/10.1016/j.ijimpeng.2022.104231 doi: 10.1016/j.ijimpeng.2022.104231
|
| [185] |
Wu L, Huang D (2022) Energy dissipation study in impact: From elastic and elastoplastic analysis in peridynamics. Int J Solids Struct 234: 111279. https://doi.org/10.1016/j.ijsolstr.2021.111279 doi: 10.1016/j.ijsolstr.2021.111279
|
| [186] |
Jafaraghaei Y, Yu T, Bui TQ (2022) Peridynamics simulation of impact failure in glass plates. Theor Appl Fract Mec 121: 103424. https://doi.org/10.1016/j.tafmec.2022.103424 doi: 10.1016/j.tafmec.2022.103424
|
| [187] | Candas A, Oterkus E, Imrak CE (2024) Modelling and analysis of wire ropes subjected to transverse impact load using peridynamic theory. J Fac Eng Archit Gaz 39: 847–858. |
| [188] |
Xu Y, Zhu P, Wang W (2023) Study of multiple impact behaviors of CFRP based on peridynamics. Compos Struct 322: 117380. https://doi.org/10.1016/j.compstruct.2023.117380 doi: 10.1016/j.compstruct.2023.117380
|
| [189] |
Zhang J, Liu X, Yang QS (2023) A unified elasto-viscoplastic peridynamics model for brittle and ductile fractures under high-velocity impact loading. Int J Impact Eng 173: 104471. https://doi.org/10.1016/j.ijimpeng.2022.104471 doi: 10.1016/j.ijimpeng.2022.104471
|
| [190] |
Lu D, Song Z, Wang G, et al. (2023) Viscoelastic peridynamic fracture analysis for concrete beam with initial crack under impact. Theor Appl Fract Mec 124: 103757. https://doi.org/10.1016/j.tafmec.2023.103757 doi: 10.1016/j.tafmec.2023.103757
|
| [191] |
Cheng Z, Zhang J, Tang J, et al. (2024) Peridynamic model of ECC-concrete composite beam under impact loading. Eng Fract Mech 295: 109791. https://doi.org/10.1016/j.engfracmech.2023.109791 doi: 10.1016/j.engfracmech.2023.109791
|
| [192] |
Alebrahim R (2019) Peridynamic modeling of Lamb wave propagation in bimaterial plates. Compos Struct 214: 12–22. https://doi.org/10.1016/j.compstruct.2019.01.108 doi: 10.1016/j.compstruct.2019.01.108
|
| [193] |
Nguyen HA, Wang H, Tanaka S, et al. (2022) An in-depth investigation of bimaterial interface modeling using ordinary state-based peridynamics. J Peridyn Nonlocal Model 4: 112–138. https://doi.org/10.1007/s42102-021-00058-x doi: 10.1007/s42102-021-00058-x
|
| [194] |
Zhang H, Zhang X, Liu Y, et al. (2022) Peridynamic modeling of elastic bimaterial interface fracture. Comput Method Appl M 390: 114458. https://doi.org/10.1016/j.cma.2021.114458 doi: 10.1016/j.cma.2021.114458
|
| [195] |
Wu WP, Li ZZ, Chu X (2023) Peridynamics study on crack propagation and failure behavior in Ni/Ni3Al bi-material structure. Compos Struct 323: 117453. https://doi.org/10.1016/j.compstruct.2023.117453 doi: 10.1016/j.compstruct.2023.117453
|
| [196] |
Wang W, Zhu QZ, Ni T, et al. (2023) Numerical simulation of interfacial and subinterfacial crack propagation by using extended peridynamics. Comput Struct 279: 106971. https://doi.org/10.1016/j.compstruc.2023.106971 doi: 10.1016/j.compstruc.2023.106971
|
| [197] | Masoumi A, Salehi M, Ravandi M (2023) Modified bond-based peridynamic approach for modeling the thermoviscoelastic response of bimaterials with viscoelastic–elastic interface. Eng Comput. https://doi.org/10.1007/s00366-023-01882-z |
| [198] |
Liu S, Fang G, Liang J, et al. (2020) A new type of peridynamics: Element-based peridynamics. Comput Method Appl M 366: 113098. https://doi.org/10.1016/j.cma.2020.113098 doi: 10.1016/j.cma.2020.113098
|
| [199] |
Imachi M, Takei T, Ozdemir M, et al. (2021) A smoothed variable horizon peridynamics and its application to the fracture parameters evaluation. Acta Mech 232: 533–553. https://doi.org/10.1007/s00707-020-02863-9 doi: 10.1007/s00707-020-02863-9
|
| [200] |
Xia Y, Meng X, Shen G, et al. (2021) Isogeometric analysis of cracks with peridynamics. Comput Method Appl M 377: 113700. https://doi.org/10.1016/j.cma.2021.113700 doi: 10.1016/j.cma.2021.113700
|
| [201] |
Javili A, McBride AT, Steinmann P (2021) A geometrically exact formulation of peridynamics. Theor Appl Fract Mec 111: 102850. https://doi.org/10.1016/j.tafmec.2020.102850 doi: 10.1016/j.tafmec.2020.102850
|
| [202] |
Yang Z, Oterkus E, Oterkus S, et al. (2023) Double horizon peridynamics. Math Mech Solids 28: 2531–2549. https://doi.org/10.1016/j.cma.2016.12.031 doi: 10.1016/j.cma.2016.12.031
|
| [203] |
Wang B, Oterkus S, Oterkus E (2023) Derivation of dual horizon state-based peridynamics formulation based on Euler-Lagrange equation. Continuum Mech Therm 35: 841–861. https://doi.org/10.1007/s00161-020-00915-y doi: 10.1007/s00161-020-00915-y
|
| [204] |
Chen H (2018) Bond-associated deformation gradients for peridynamic correspondence model. Mec Res Commun 90: 34–41. https://doi.org/10.1016/j.mechrescom.2018.04.004 doi: 10.1016/j.mechrescom.2018.04.004
|
| [205] |
Madenci E, Dorduncu M, Phan N, et al. (2019) Weak form of bond-associated non-ordinary state-based peridynamics free of zero energy modes with uniform or non-uniform discretization. Eng Fract Mech 218: 106613. https://doi.org/10.1016/j.engfracmech.2019.106613 doi: 10.1016/j.engfracmech.2019.106613
|
| [206] |
Jafarzadeh S, Mousavi F, Larios A, et al. (2022) A general and fast convolution-based method for peridynamics: Applications to elasticity and brittle fracture. Comput Method Appl M 392: 114666. https://doi.org/10.1016/j.cma.2022.114666 doi: 10.1016/j.cma.2022.114666
|
| [207] |
Gu X, Zhang Q, Madenci E (2019) Non-ordinary state-based peridynamic simulation of elastoplastic deformation and dynamic cracking of polycrystal. Eng Fract Mech 218: 106568. https://doi.org/10.1016/j.engfracmech.2019.106568 doi: 10.1016/j.engfracmech.2019.106568
|
| [208] |
Gur S, Sadat MR, Frantziskonis GN, et al. (2019) The effect of grain-size on fracture of polycrystalline silicon carbide: A multiscale analysis using a molecular dynamics-peridynamics framework. Comp Mater Sci 159: 341–348. https://doi.org/10.1016/j.commatsci.2018.12.038 doi: 10.1016/j.commatsci.2018.12.038
|
| [209] |
Li M, Oterkus S, Oterkus E (2020) Investigation of the effect of porosity on intergranular brittle fracture using peridynamics. Procedia Struct Integr 28: 472–481. https://doi.org/10.1016/j.prostr.2020.10.056 doi: 10.1016/j.prostr.2020.10.056
|
| [210] |
Li M, Lu W, Oterkus E, et al. (2020) Thermally-induced fracture analysis of polycrystalline materials by using peridynamics. Eng Anal Bound Elem 117: 167–187. https://doi.org/10.1016/j.enganabound.2020.04.016 doi: 10.1016/j.enganabound.2020.04.016
|
| [211] |
Zhu J, He X, Yang D, et al. (2021) A peridynamic model for fracture analysis of polycrystalline BCC-Fe associated with molecular dynamics simulation. Theor Appl Fract Mec 114: 102999. https://doi.org/10.1016/j.tafmec.2021.102999 doi: 10.1016/j.tafmec.2021.102999
|
| [212] |
Premchander A, Amin I, Oterkus S, et al. (2022) Peridynamic modelling of propagation of cracks in photovoltaic panels. Procedia Struct Integr 41: 305–316. https://doi.org/10.1016/j.prostr.2022.05.036 doi: 10.1016/j.prostr.2022.05.036
|
| [213] |
Chen Z, Niazi S, Bobaru F (2019) A peridynamic model for brittle damage and fracture in porous materials. Int J Rock Mech Min 122: 104059. https://doi.org/10.1016/j.ijrmms.2019.104059 doi: 10.1016/j.ijrmms.2019.104059
|
| [214] |
Shen S, Yang Z, Han F, et al. (2021) Peridynamic modeling with energy-based surface correction for fracture simulation of random porous materials. Theor Appl Fract Mec 114: 102987. https://doi.org/10.1016/j.tafmec.2021.102987 doi: 10.1016/j.tafmec.2021.102987
|
| [215] |
Ni T, Sanavia L, Zaccariotto M, et al. (2022) Fracturing dry and saturated porous media, peridynamics and dispersion. Comput Geotech 151: 104990. https://doi.org/10.1016/j.compgeo.2022.104990 doi: 10.1016/j.compgeo.2022.104990
|
| [216] |
Ozdemir M, Oterkus S, Oterkus E, et al. (2023) Evaluation of dynamic behaviour of porous media including micro-cracks by ordinary state-based peridynamics. Eng Comput 39: 61–79. https://doi.org/10.1007/s00366-021-01506-4 doi: 10.1007/s00366-021-01506-4
|
| [217] |
Shangkun S, Zihao Y, Junzhi C, et al. (2023) Dual-variable-horizon peridynamics and continuum mechanics coupling modeling and adaptive fracture simulation in porous materials. Eng Comput 39: 3207–3227. https://doi.org/10.1007/s00366-022-01730-6 doi: 10.1007/s00366-022-01730-6
|
| [218] |
Gu X, Li X, Xia X, et al. (2023) A robust peridynamic computational framework for predicting mechanical properties of porous quasi-brittle materials. Compos Struct 303: 116245. https://doi.org/10.1016/j.compstruct.2022.116245 doi: 10.1016/j.compstruct.2022.116245
|
| [219] | Altay U, Dorduncu M, Kadioglu S (2024) Dual horizon peridynamic approach for studying the effect of porous media on the dynamic crack growth in brittle materials. J Peridyn Nonlocal Model. https://doi.org/10.1007/s42102-023-00115-7 |
| [220] |
Yan H, Sedighi M, Jivkov AP (2020) Peridynamics modelling of coupled water flow and chemical transport in unsaturated porous media. J Hydrol 591: 125648. https://doi.org/10.1016/j.jhydrol.2020.125648 doi: 10.1016/j.jhydrol.2020.125648
|
| [221] |
Katiyar A, Agrawal S, Ouchi H, et al. (2020) A general peridynamics model for multiphase transport of non-Newtonian compressible fluids in porous media. J Comput Phys 402: 109075. https://doi.org/10.1016/j.jcp.2019.109075 doi: 10.1016/j.jcp.2019.109075
|
| [222] |
Sun W, Fish J (2021) Coupling of non-ordinary state-based peridynamics and finite element method for fracture propagation in saturated porous media. Int J Numer Anal Met 45: 1260–1281. https://doi.org/10.1002/nag.3200 doi: 10.1002/nag.3200
|
| [223] |
Ni T, Pesavento F, Zaccariotto M, et al. (2021) Numerical simulation of forerunning fracture in saturated porous solids with hybrid fem/peridynamic model. Comput Geotech 133: 104024. https://doi.org/10.1016/j.compgeo.2021.104024 doi: 10.1016/j.compgeo.2021.104024
|
| [224] |
Galadima Y, Oterkus E, Oterkus S (2019) Two-dimensional Implementation of the coarsening method for linear peridynamics. AIMS Mater Sci 6: 252–275. 10.3934/matersci.2019.2.252 doi: 10.3934/matersci.2019.2.252
|
| [225] |
Galadima YK, Oterkus E, Oterkus S (2021) Model order reduction of linear peridynamic systems using static condensation. Math Mech Solids 26: 552–569. https://doi.org/10.1177/1081286520937045 doi: 10.1177/1081286520937045
|
| [226] |
Galadima YK, Oterkus E, Oterkus S (2022) Static condensation of peridynamic heat conduction model. Math Mech Solids 27: 2689–2714. https://doi.org/10.1177/10812865221081160 doi: 10.1177/10812865221081160
|
| [227] |
Dong H, Wang H, Jiang G, et al. (2023) An adaptive partitioned reduced order model of peridynamics for efficient static fracture simulation. Eng Anal Bound Elem 157: 191–206. https://doi.org/10.1016/j.enganabound.2023.09.007 doi: 10.1016/j.enganabound.2023.09.007
|
| [228] |
Zhao T, Shen Y (2023) A reduced-order peridynamic model for predicting nonlocal heat conduction in nanocomposites. Compos Struct 323: 117477. https://doi.org/10.1016/j.compstruct.2023.117477 doi: 10.1016/j.compstruct.2023.117477
|
| [229] |
Dai MJ, Tanaka S, Oterkus S, et al. (2020) Mixed-mode stress intensity factors evaluation for flat shells under in-plane loading employing ordinary state-based peridynamics. Theor Appl Fract Mec 112: 102841. https://doi.org/10.1016/j.tafmec.2020.102841 doi: 10.1016/j.tafmec.2020.102841
|
| [230] |
Zhu N, Oterkus E (2020) Calculation of stress intensity factor using displacement extrapolation method in peridynamic framework. J Mech 36: 235–243. https://doi.org/10.1017/jmech.2019.62 doi: 10.1017/jmech.2019.62
|
| [231] |
Le MQ (2023) Mode-Ⅰ stress intensity factor by peridynamic stresses. Theor Appl Fract Mec 123: 103721. https://doi.org/10.1016/j.tafmec.2022.103721 doi: 10.1016/j.tafmec.2022.103721
|
| [232] |
Wang H, Tanaka S, Oterkus S, et al. (2023) Evaluation of stress intensity factors under thermal effect employing domain integral method and ordinary state based peridynamic theory. Continuum Mech Therm 35: 1021–1040. https://doi.org/10.1007/s00161-021-01033-z doi: 10.1007/s00161-021-01033-z
|
| [233] |
Kefal A, Diyaroglu C, Yildiz M, et al. (2022) Coupling of peridynamics and inverse finite element method for shape sensing and crack propagation monitoring of plate structures. Comput Method Appl M 391: 114520. https://doi.org/10.1016/j.cma.2021.114520 doi: 10.1016/j.cma.2021.114520
|
| [234] |
Oterkus S, Oterkus E (2023) Peridynamic surface elasticity formulation based on modified core-shell model. J Peridyn Nonlocal Model 5: 229–240. https://doi.org/10.1007/s42102-022-00089-y doi: 10.1007/s42102-022-00089-y
|
| [235] |
Javili A, Ekiz E, McBride AT, et al. (2021) Continuum-kinematics-inspired peridynamics: Thermo-mechanical problems. Continuum Mech Therm 33: 2039–2063. https://doi.org/10.1007/s00161-021-01000-8 doi: 10.1007/s00161-021-01000-8
|
| [236] |
Pathrikar A, Tiwari SB, Arayil P, et al. (2021) Thermomechanics of damage in brittle solids: A peridynamics model. Theor Appl Fract Mec 112: 102880. https://doi.org/10.1016/j.tafmec.2020.102880 doi: 10.1016/j.tafmec.2020.102880
|
| [237] |
Wang B, Oterkus S, Oterkus E (2021) Thermal diffusion analysis by using dual horizon peridynamics. J Therm Stresses 44: 51–74. https://doi.org/10.1080/01495739.2020.1843378 doi: 10.1080/01495739.2020.1843378
|
| [238] |
Chen W, Gu X, Zhang Q, et al. (2021) A refined thermo-mechanical fully coupled peridynamics with application to concrete cracking. Eng Fract Mech 242: 107463. https://doi.org/10.1016/j.engfracmech.2020.107463 doi: 10.1016/j.engfracmech.2020.107463
|
| [239] |
Martowicz A, Kantor S, Pieczonka Ł, et al. (2021) Phase transformation in shape memory alloys: A numerical approach for thermomechanical modeling via peridynamics. Meccanica 56: 841–854. https://doi.org/10.1007/s11012-020-01276-1 doi: 10.1007/s11012-020-01276-1
|
| [240] |
Wang B, Oterkus S, Oterkus E (2022) Thermomechanical phase change peridynamic model for welding analysis. Eng Anal Bound Elem 140: 371–385. https://doi.org/10.1016/j.enganabound.2022.04.030 doi: 10.1016/j.enganabound.2022.04.030
|
| [241] |
Liu QQ, Wu D, Madenci E, et al. (2022) State-based peridynamics for thermomechanical modeling of fracture mechanisms in nuclear fuel pellets. Eng Fract Mech 276: 108917. https://doi.org/10.1016/j.engfracmech.2022.108917 doi: 10.1016/j.engfracmech.2022.108917
|
| [242] |
Zhang J, Guo L (2023) A fully coupled thermo-mechanical peridynamic model for cracking analysis of frozen rocks. Comput Geotech 164: 105809. https://doi.org/10.1016/j.compgeo.2023.105809 doi: 10.1016/j.compgeo.2023.105809
|
| [243] |
Sun WK, Yin BB, Akbar A, et al. (2024) A coupled 3D thermo-mechanical peridynamic model for cracking analysis of homogeneous and heterogeneous materials. Comput Method Appl M 418: 116577. https://doi.org/10.1016/j.cma.2023.116577 doi: 10.1016/j.cma.2023.116577
|
| [244] |
Nikolaev P, Jivkov AP, Fifre M, et al. (2024) Peridynamic analysis of thermal behaviour of PCM composites for heat storage. Comput Method Appl M 424: 116905. https://doi.org/10.1016/j.cma.2024.116905 doi: 10.1016/j.cma.2024.116905
|
| [245] |
Wen Z, Hou C, Zhao M, et al. (2023) A peridynamic model for non-Fourier heat transfer in orthotropic plate with uninsulated cracks. Appl Math Model 115: 706–723. https://doi.org/10.1016/j.apm.2022.11.010 doi: 10.1016/j.apm.2022.11.010
|
| [246] | Abdoh DA (2024) Peridynamic modeling of transient heat conduction in solids using a highly efficient algorithm. Numer Heat Tr B-Fund 1–16. https://doi.org/10.1080/10407790.2024.2310708 |
| [247] |
Kefal A, Sohouli A, Oterkus E, et al. (2019) Topology optimization of cracked structures using peridynamics. Continuum Mech Therm 31: 1645–1672. https://doi.org/10.1007/s00161-019-00830-x doi: 10.1007/s00161-019-00830-x
|
| [248] |
Oh M, Koo B, Kim JH, et al. (2021) Shape design optimization of dynamic crack propagation using peridynamics. Eng Fract Mech 252: 107837. https://doi.org/10.1016/j.engfracmech.2021.107837 doi: 10.1016/j.engfracmech.2021.107837
|
| [249] |
Silling SA (2019) Attenuation of waves in a viscoelastic peridynamic medium. Math Mech Solids 24: 3597–3613. https://doi.org/10.1177/1081286519847241 doi: 10.1177/1081286519847241
|
| [250] |
Behera D, Roy P, Madenci E (2021) Peridynamic modeling of bonded-lap joints with viscoelastic adhesives in the presence of finite deformation. Comput Method Appl M 374: 113584. https://doi.org/10.1016/j.cma.2020.113584 doi: 10.1016/j.cma.2020.113584
|
| [251] |
Yu H, Chen X (2021) A viscoelastic micropolar peridynamic model for quasi-brittle materials incorporating loading-rate effects. Comput Method Appl M 383: 113897. https://doi.org/10.1016/j.cma.2021.113897 doi: 10.1016/j.cma.2021.113897
|
| [252] |
Ozdemir M, Oterkus S, Oterkus E, et al. (2022) Fracture simulation of viscoelastic membranes by ordinary state-based peridynamics. Procedia Struct Integr 41: 333–342. https://doi.org/10.1016/j.prostr.2022.05.039 doi: 10.1016/j.prostr.2022.05.039
|
| [253] |
Huang Y, Oterkus S, Hou H, et al. (2022) Peridynamic model for visco-hyperelastic material deformation in different strain rates. Continuum Mech Therm 34: 977–1011. https://doi.org/10.1007/s00161-019-00849-0 doi: 10.1007/s00161-019-00849-0
|
| [254] |
Tian DL, Zhou XP (2022) A viscoelastic model of geometry-constraint-based non-ordinary state-based peridynamics with progressive damage. Comput Mech 69: 1413–1441. https://doi.org/10.1007/s00466-022-02148-z doi: 10.1007/s00466-022-02148-z
|
| [255] |
Azizi MA, Mohd Zahari MZ, Abdul Rahim S, et al. (2022) Fracture analysis for viscoelastic creep using peridynamic formulation. J Theor Appl Mech 60: 579–591. https://doi.org/10.15632/jtam-pl/152712 doi: 10.15632/jtam-pl/152712
|
| [256] |
Galadima YK, Oterkus S, Oterkus E, et al. (2023) Modelling of viscoelastic materials by using non-ordinary state-based peridynamics. Eng Comput 40: 527–540. https://doi.org/10.1007/s00366-023-01808-9 doi: 10.1007/s00366-023-01808-9
|
| [257] |
Zhang X, Xu Z, Yang Q (2019) Wave dispersion and propagation in linear peridynamic media. Shock Vib 2019: 1–9. https://doi.org/10.1155/2019/9528978 doi: 10.1155/2019/9528978
|
| [258] |
Wang B, Oterkus S, Oterkus E (2020) Closed-form dispersion relationships in bond-based peridynamics. Procedia Struct Integr 28: 482–490. https://doi.org/10.1016/j.prostr.2020.10.057 doi: 10.1016/j.prostr.2020.10.057
|
| [259] |
Li S, Jin Y, Lu H, et al. (2021) Wave dispersion and quantitative accuracy analysis of bond-based peridynamic models with different attenuation functions. Comp Mater Sci 197: 110667. https://doi.org/10.1016/j.commatsci.2021.110667 doi: 10.1016/j.commatsci.2021.110667
|
| [260] |
Oterkus S, Oterkus E (2023) Comparison of peridynamics and lattice dynamics wave dispersion relationships. J Peridyn Nonlocal Model 5: 461–471. https://doi.org/10.1007/s42102-022-00087-0 doi: 10.1007/s42102-022-00087-0
|
| [261] |
Alebrahim R, Packo P, Zaccariotto M, et al. (2022) Improved wave dispersion properties in 1D and 2D bond-based peridynamic media. Comp Part Mech 9: 597–614. https://doi.org/10.1007/s40571-021-00433-x doi: 10.1007/s40571-021-00433-x
|
| [262] | Wang B, Oterkus S, Oterkus E (2023) Closed-form wave dispersion relationships for ordinary state-based peridynamics. J Peridyn Nonlocal Model. https://doi.org/10.1007/s42102-023-00109-5 |
| 1. | Erkan Oterkus, Timon Rabczuk, Selda Oterkus, Special Issue: Peridynamics and its applications, 2024, 11, 2372-0484, 602, 10.3934/matersci.2024030 | |
| 2. | Zhenghao Yang, Chien‐Ching Ma, Konstantin Naumenko, Holm Altenbach, Plate buckling analysis in peridynamic framework, 2024, 0044-2267, 10.1002/zamm.202400380 | |
| 3. | Alvina Oksanchenko, Konstantin Naumenko, 2025, Chapter 1, 978-3-031-79092-8, 3, 10.1007/978-3-031-79093-5_1 | |
| 4. | Konstantin Naumenko, Zhenghao Yang, First order shear deformation beam theories in a peridynamic framework, 2025, 112, 09977538, 105633, 10.1016/j.euromechsol.2025.105633 |
Erkan Oterkus, Selda Oterkus. Recent advances in peridynamic theory: A review[J]. AIMS Materials Science, 2024, 11(3): 515-546. doi: 10.3934/matersci.2024026
DownLoad:
