A time-stepping BEM for three-dimensional thermoelastic fracture problems of anisotropic functionally graded materials

Mohamed Abdelsabour Fahmy; Ahmad Almutlg; Mohamed Abdelsabour Fahmy; Ahmad Almutlg

doi:10.3934/math.2025197

AIMS Mathematics

2025, Volume 10, Issue 2: 4268-4285. doi: 10.3934/math.2025197

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A time-stepping BEM for three-dimensional thermoelastic fracture problems of anisotropic functionally graded materials

Mohamed Abdelsabour Fahmy ^{1
,
,},
Ahmad Almutlg ²

1.
Department of Mathematics, Adham University College, Umm Al-Qura University, Adham 28653, Makkah, Saudi Arabia
2.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Received: 31 October 2024 Revised: 09 February 2025 Accepted: 25 February 2025 Published: 28 February 2025
MSC : 65M38, 78M15, 80M15

The primary goal of this study is to create a novel mathematical model based on the time-stepping boundary element method (BEM) scheme for solving three-dimensional coupled dynamic thermoelastic fracture issues in anisotropic functionally graded materials (FGMs). The crack tip opening displacement determines the dynamic stress intensity factor (SIF). The effects of anisotropy, graded parameters, and angle locations on the SIF were studied for three-dimensional coupled dynamic thermoelastic fracture situations. The results show that the novel method is exceptionally exact and efficient at assessing the fracture mechanics of fractured thermoelastic anisotropic FGMs. In addition, this paper provides a theoretical framework for analyzing a wide range of real engineering applications.
- mathematical model,
- boundary element method,
- dynamic thermoelasticity,
- fracture problems,
- anisotropic functionally graded materials,
- stress intensity factor
Citation: Mohamed Abdelsabour Fahmy, Ahmad Almutlg. A time-stepping BEM for three-dimensional thermoelastic fracture problems of anisotropic functionally graded materials[J]. AIMS Mathematics, 2025, 10(2): 4268-4285. doi: 10.3934/math.2025197

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Abstract

The primary goal of this study is to create a novel mathematical model based on the time-stepping boundary element method (BEM) scheme for solving three-dimensional coupled dynamic thermoelastic fracture issues in anisotropic functionally graded materials (FGMs). The crack tip opening displacement determines the dynamic stress intensity factor (SIF). The effects of anisotropy, graded parameters, and angle locations on the SIF were studied for three-dimensional coupled dynamic thermoelastic fracture situations. The results show that the novel method is exceptionally exact and efficient at assessing the fracture mechanics of fractured thermoelastic anisotropic FGMs. In addition, this paper provides a theoretical framework for analyzing a wide range of real engineering applications.

References

[1]	S. Zghal, F. Dammak, Functionally Graded Materials: Analysis and Applications to FGM, FG-CNTRC and FG Porous Structures, Boca Raton, Florida: CRC press, 2024. https://doi.org/10.1201/9781003483786
[2]	S. Zghal, D. Ataoui, F. Dammak, Free vibration analysis of porous beams with gradually varying mechanical properties. Proceedings of the Institution of Mechanical Engineers, P. I. Mech. Eng. M. -J. Eng., 236 (2022), 800–812. https://doi.org/10.1177/14750902211047746 doi: 10.1177/14750902211047746
[3]	S. Trabelsi, S. Zghal, F. Dammak, Thermo-elastic buckling and post-buckling analysis of functionally graded thin plate and shell structures, J. Braz. Soc. Mech. Sci. Eng., 42 (2020), 233. https://doi.org/10.1007/s40430-020-02314-5 doi: 10.1007/s40430-020-02314-5
[4]	N. Joueid, S. Zghal, M. Chrigui, F. Dammak, Thermoelastic buckling analysis of plates and shells of temperature and porosity dependent functionally graded materials, Mech. Time-Depend. Mater., 28 (2024), 817–859. https://doi.org/10.1007/s11043-023-09644-6 doi: 10.1007/s11043-023-09644-6
[5]	M. A. Fahmy, M. Toujani, A New Fractional Boundary Element Model for the 3D Thermal Stress Wave Propagation Problems in Anisotropic Materials, Math. Comput. Appl., 30 (2025), 6. https://doi.org/10.3390/mca30010006 doi: 10.3390/mca30010006
[6]	M. A. Fahmy, Three-dimensional boundary element sensitivity analysis of anisotropic thermoelastic materials, J. Umm Al-Qura Univ. Appl. Sci., (2025). https://doi.org/10.1007/s43994-024-00210-5
[7]	F. Delale, F. Erdogan, The crack problem for a nonhomogeneous plane, J. Appl. Mech., 50 (1983), 609–614. https://doi.org/10.1115/1.3167098 doi: 10.1115/1.3167098
[8]	L. C. Guo, N. Noda, Modeling method for a crack problem of functionally graded materials with arbitrary properties piecewise-exponential model, Int. J. Solids Struct., 44 (2007), 6768–6790. https://doi.org/10.1016/j.ijsolstr.2007.03.012 doi: 10.1016/j.ijsolstr.2007.03.012
[9]	F. Erdogan, B. H. Wu, Crack problems in FGM layers under thermal stresses, J. Therm. Stresses, 19 (1996), 237–265. https://doi.org/10.1080/01495739608946172 doi: 10.1080/01495739608946172
[10]	N. Noda, Z. H. Jin, Thermal stresses intensity factors for a crack in a strip of a functionally graded material, Int. J. Solids Struct., 30 (1993), 1039–1056. https://doi.org/10.1016/0020-7683(93)90002-O doi: 10.1016/0020-7683(93)90002-O
[11]	N. Noda, Z. H. Jin, Thermal stresses around a crack in the nonhomogeneous interfacial layer between two dissimilar elastic half-planes, Int. J. Solids Struct., 41 (2004), 923–945. https://doi.org/10.1016/j.ijsolstr.2003.09.056 doi: 10.1016/j.ijsolstr.2003.09.056
[12]	Z. H. Jin, N. Noda, Crack-tip singular fields in non-homogeneous body with crack in thermal stress fields, J. Appl. Mech., 61 (1994), 738–740. https://doi.org/10.1115/1.2901529 doi: 10.1115/1.2901529
[13]	N. Noda, Thermal stresses intensity for functionally graded plate with an edge crack, J. Therm. Stresses, 20 (1996), 373–387. https://doi.org/10.1080/01495739708956108 doi: 10.1080/01495739708956108
[14]	K. H. Lee, Analysis of a propagating crack tip in orthotropic functionally graded materials, Compos. Part B: Eng., 84 (2016), 83–97. https://doi.org/10.1016/j.compositesb.2015.08.068 doi: 10.1016/j.compositesb.2015.08.068
[15]	Y. D. Lee, F. Erdogan, Interface Cracking of FGM Coating under Steady State Heat Flow, Eng. Fract. Mech., 59 (1998), 361–380. https://doi.org/10.1016/S0013-7944(97)00137-9 doi: 10.1016/S0013-7944(97)00137-9
[16]	P. Gu, M. Dao, R. J. Asrao, A Simplified Method for Calculating the Crack-tip Field of Functionally Graded Materials Using the Domain Integral, J. Appl. Mech., 66 (1999), 101–108. https://doi.org/10.1115/1.2789135 doi: 10.1115/1.2789135
[17]	B. N. Rao, S. Rahman, Meshfree analysis of cracks in isotropic functionally graded materials, Eng. Fract. Mech., 70 (2003), 1–27. https://doi.org/10.1016/S0013-7944(02)00038-3 doi: 10.1016/S0013-7944(02)00038-3
[18]	M. A. Fahmy, A Three-Dimensional CQBEM Model for Thermal Stress Sensitivities in Anisotropic Materials, Appl. Math. Inf. Sci. 19 (2025), 489–495. http://dx. doi.org/10.18576/amis/190301 doi: 10.18576/amis/190301
[19]	M. A. Fahmy, Three-dimensional Boundary Element Modeling for The Effect of Rotation on the Thermal Stresses of Anisotropic Materials, Appl. Math. Inf. Sci., 19 (2025), 379–386. http://dx. doi.org/10.18576/amis/190213 doi: 10.18576/amis/190213
[20]	M. A. Fahmy, BEM Modeling for Stress Sensitivity of Nonlocal Thermo-Elasto-Plastic Damage Problems, Computation, 12 (2024), 87. https://doi.org/10.3390/computation12050087 doi: 10.3390/computation12050087
[21]	M. A. Fahmy, M. Toujani, Fractional Boundary Element Solution for Nonlinear Nonlocal Thermoelastic Problems of Anisotropic Fibrous Polymer Nanomaterials, Computation, 12 (2024), 117. https://doi.org/10.3390/computation12060117 doi: 10.3390/computation12060117
[22]	M. A. Fahmy, A new boundary element model for magneto‐thermo‐elastic stress sensitivities in anisotropic functionally graded materials, J. Umm Al-Qura Univ. Eng. Archit., 2025. https://doi.org/10.1007/s43995-025-00100-9
[23]	M. A. Fahmy, A time-stepping DRBEM for nonlinear fractional sub-diffusion bio-heat ultrasonic wave propagation problems during electromagnetic radiation, J Umm Al-Qura Univ Appl Sci, 2024. https://doi.org/10.1007/s43994-024-00178-2
[24]	M. A. Fahmy, R. A. A. Jeli, A New Fractional Boundary Element Model for Anomalous Thermal Stress Effects on Cement-Based Materials, Fractal Fract., 8 (2024), 753. https://doi.org/10.3390/fractalfract8120753 doi: 10.3390/fractalfract8120753
[25]	B. Zheng, Y. Yang, X. Gao, C. Zhang, Dynamic fracture analysis of functionally graded materials under thermal shock loading by using the radial integration boundary element method, Compos. Struct., 201 (2018), 468–476. https://doi.org/10.1016/j.compstruct.2018.06.050 doi: 10.1016/j.compstruct.2018.06.050
[26]	H. A. Atmane, A. Tounsi, S. A. Meftah, H. A. Belhadj, Free vibration behavior of exponential functionally graded beams with varying cross-section, J. Vib. Control, 17 (2011), 311–318. https://doi.org/10.1177/1077546310370691 doi: 10.1177/1077546310370691
[27]	K. Yang, X. W. Gao, Radial integration BEM for transient heat conduction problems, Eng. Anal. Bound. Elem., 34 (2010), 557–563.
[28]	X. W. Gao, C. Zhang, J. Sladek, V. Sladek, Fracture analysis of functionally graded materials by a BEM, Compos. Sci. Technol., 68 (2008), 1209–1215. https://doi.org/10.1016/j.compscitech.2007.08.029 doi: 10.1016/j.compscitech.2007.08.029
[29]	X. W. Gao, Boundary element analysis in thermoelasticity with and without internal cells, Int. J. Numer. Methods Eng., 57 (2003), 957–990. https://doi.org/10.1002/nme.715 doi: 10.1002/nme.715
[30]	F. Erdogan, Fracture mechanics of functionally graded materials, Int. J. Solids Struct., 5 (1995), 753–770. https://doi.org/10.1016/0961-9526(95)00029-M doi: 10.1016/0961-9526(95)00029-M
[31]	P. N. J. Rasolofosaon, B. E. Zinszner, Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks, Geophysics, 67 (2002), 230–240. https://doi.org/10.1190/1.1451647 doi: 10.1190/1.1451647
[32]	M. D. Iqbal, C. Birk, E. T. Ooi, S. Natarajan, H. Gravenkamp, Transient thermoelastic fracture analysis of functionally graded materials using the scaled boundary finite element method, Theor. Appl. Fract. Mec., 127 (2023), 104056. https://doi.org/10.1016/j.tafmec.2023.104056 doi: 10.1016/j.tafmec.2023.104056
[33]	E. Pan, Exact Solution for Functionally Graded Anisotropic Elastic Composite Laminates, J. Compos. Mater., 37 (2003), 1903–1920. https://doi.org/10.1177/002199803035565 doi: 10.1177/002199803035565

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