Search Advanced

AIMS Materials Science

2024, Volume 11, Issue 3: 515-546. doi: 10.3934/matersci.2024026
Previous Article Next Article
Review Special Issues

Recent advances in peridynamic theory: A review

  • Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, 100 Montrose Street, Glasgow, G4 0LZ, UK
  • Received: 06 April 2024 Revised: 26 April 2024 Accepted: 29 April 2024 Published: 21 May 2024

  • 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

    Related Papers:

  • 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.


    加载中


    [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
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Materials Science
1.4 3.6

Metrics

Article views(1645) PDF downloads(390) Cited by(2)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Figures(1)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog