Abstract
Nodal stresses are exploited in peridynamics to investigate the mode-I J-integral of single edge- and center-cracked plates with initial crack length-plate width ratios from 0.1 through 0.5. Computed values of the J-integral on six different contours differ from each other by about 1% and are compared and discussed with analytical methods, with finite element analysis as well as with previous peridynamic studies. Simulation results show that mode-I J-integral via peridynamic stresses are highly accurate.
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References
Anderson TL (2017) Fracture mechanics: fundamentals and applications. CRC Press, Taylor & Francis Group, Boca Raton
Ayachit U (2015) The paraview guide: a parallel visualization application. Kitware Inc., New York
Breitenfeld MS, Geubelle PH, Weckner O, Silling S (2014) Non-ordinary state-based peridynamic analysis of stationary crack problems. Comput Methods Appl Mech Eng 272:233–250
Fallah AS, Giannakeas IN, Mella R, Wenman MR, Safa Y, Bahai H (2020) On the computational derivation of bond-based peridynamic stress tensor. J Peridynamics Nonlocal Model 2(4):352–378
Hu W, Ha YD, Bobaru F, Silling SA (2012) The formulation and computation of the nonlocal J-integral in bond-based peridynamics. Int J Fract 176(2):195–206
Imachi M, Tanaka S, Bui TQ (2018) Mixed-mode dynamic stress intensity factors evaluation using ordinary state-based peridynamics. Theoret Appl Fract Mech 93:97–104
Khandelwal N, Murthy AR (2022) Fracture analysis of single edge notched specimen using phase field approach. Structures 37:756–771
Kilic B, Madenci E (2010) An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory. Theoret Appl Fract Mech 53(3):194–204
Le M-Q (2023) Mode-I stress intensity factor by peridynamic stresses. Theoret Appl Fract Mech 123:103721
Li J, Li S, Lai X, Liu L (2022) Peridynamic stress is the static first Piola-Kirchhoff virial stress. Int J Solids Struct 241:111478
Madenci E, Oterkus E (2014) Peridynamic theory and its applications. Springer
Marc G, McMillan WG (1985) The virial theorem. Adv Chem Phys 58:209
Panchadhara R, Gordon PA (2016) Application of peridynamic stress intensity factors to dynamic fracture initiation and propagation. Int J Fract 201(1):81–96
Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech Trans ASME 35(2):379–386
Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–209
Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17–18):1526–1535
Silling SA, Lehoucq RB (2010) Peridynamic theory of solid mechanics. Adv Appl Mech 44:73–168
Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88(2):151–184
Soliman ESMM (2022) Mode I stress intensity factor with various crack types. Frattura Ed Integrità Strutturale 16(59):471–485
Stenström C, Eriksson K (2019) The J-contour integral in peridynamics via displacements. Int J Fract 216(2):173–183
Stenström C, Eriksson K (2021) The J-area integral applied in peridynamics. Int J Fract 228(2):127–142
Tada H (1971) A note on the finite width corrections to the stress intensity factor. Eng Fract Mech 3(3):345–347
Tada H, Paris PC, Irwin GR (2000) The stress analysis of cracks handbook. ASME Press, USA
Zhang H, Qiao P (2020a) On the computation of energy release rates by a peridynamic virtual crack extension method. Comput Methods Appl Mech Eng 363:112883
Zhang H, Qiao P (2020b) Virtual crack closure technique in peridynamic theory. Comput Methods Appl Mech Eng 372:113318
Zhu N, Oterkus E (2020) Calculation of stress intensity factor using displacement extrapolation method in peridynamic framework. J Mech 36(2):235–243
Zimmerman JA, Hoyt JJ, Jones RE, Klein PA, Bammann DJ (2004) Calculation of stress in atomistic simulation. Model Simul Mater Sci Eng 12:S319–S332
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Le, MQ. Mode-I J-integral via peridynamic stresses. Int J Fract 241, 143–151 (2023). https://doi.org/10.1007/s10704-023-00691-1
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DOI: https://doi.org/10.1007/s10704-023-00691-1