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Bond- and state-based peridynamic analysis in a commercial finite element framework with native elements. (English) Zbl 1507.74045

Summary: This study presents a framework to perform bond-based (BB), ordinary state-based (OSB) and non-ordinary state-based (NOSB) peridynamic (PD) analysis in ANSYS, a commercial software, with native MATRIX27 elements. The PD equilibrium equations as well as the PD form of the traction components are constructed by using these elements and solved within the ANSYS framework through implicit methods. The domain is divided into three regions in order to satisfy the equilibrium equations and to directly impose the displacement and traction boundary conditions without a fictitious layer. The results are free of displacement kinks; thus, removing the unphysical stress concentrations. Also, the displacement predictions maintain the smoothness throughout the domain. Its accuracy is demonstrated by considering isotropic elastic plates subjected to various types of boundary conditions under quasi-static loading conditions. For all combinations of boundary conditions, the displacement predictions agree well with FE results. Failure is introduced gradually through the KILL option in ANSYS.

MSC:

74A60 Micromechanical theories

Software:

ANSYS
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References:

[1] Silling, S. A., Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids, 48, 175-209 (2000) · Zbl 0970.74030
[2] Silling, S. A.; Epton, M.; Weckner, O.; Xu, J.; Askari, E., Peridynamic states and constitutive modeling, J. Elasticity, 88, 151-184 (2007) · Zbl 1120.74003
[3] Silling, S. A.; Lehoucq, R. B., Peridynamic theory of solid mechanics, Adv. Appl. Mech., 44, 73-168 (2010)
[4] Madenci, E., Peridynamic integrals for strain invariants of homogeneous deformation, ZAMM J. Appl. Math. Mech., 97, 1236-1251 (2017)
[5] Madenci, E.; Oterkus, E., Peridynamic Theory and its Applications (2014), Springer: Springer New York, NY · Zbl 1295.74001
[6] Gu, X.; Madenci, E.; Zhang, Q., Revisit of non-ordinary state-based peridynamics, Eng. Fract. Mech., 190, 31-52 (2017)
[7] Chen, H.; Spencer, B. W., Peridynamic bond-associated correspondence model: Stability and convergence properties, Internat. J. Numer. Methods Engrg., 117, 713-727 (2019)
[8] Ren, H.; Zhuang, X.; Cai, Y.; Rabczuk, T., Dual horizon peridynamics, Internat. J. Numerical Methods Eng., 108, 12, 1451-1476 (2016)
[9] Ren, H.; Zhuang, X.; Rabczuk, T., Dual-horizon peridynamics: a stable solution to varying horizons, Comput. Methods Appl. Mech. Eng., 318, 762-782 (2017) · Zbl 1439.74030
[10] Macek, R. W.; Silling, S. A., Peridynamics via finite element analysis, Finite Elem. Anal. Des., 43, 1169-1178 (2007)
[11] Sarego, G.; Le, Q. V.; Bobaru, F.; Zaccariotto, M.; Galvanetto, U., Linearized state-based peridynamics for 2-D problems, Internat. J. Numer. Methods Engrg., 108, 1174-1197 (2016)
[12] Madenci, E.; Oterkus, S., Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening, J. Mech. Phys. Solids, 86, 192-219 (2016)
[13] Zhao, J.; Jafarzadeh, S.; Chen, Z.; Bobaru, F., An algorithm for imposing local boundary conditions in peridynamic models on arbitrary domains (2020), engrXiv
[14] Prudhomme, S.; Diehl, P., On the treatment of boundary conditions for bond-based peridynamic models, Comput. Methods Appl. Mech. Engrg., 372, Article 113391 pp. (2020) · Zbl 1506.74433
[15] Chen, J.; Jiao, Y.; Jiang, W.; Zhang, Y., Peridynamics boundary condition treatments via the pseudo-layer enrichment method and variable horizon approach, Math. Mech. Solids, 26, 631-666 (2020) · Zbl 07357420
[16] Scabbia, F.; Zaccariotto, M.; Galvanetto, U., A novel and effective way to impose boundary conditions and to mitigate the surface effect in state-based peridynamics, Internat. J. Numer. Methods Engrg., 122, 5773-5811 (2021)
[17] Behera, D.; Roy, P.; Anicode, S. V.K.; Madenci, E.; Spencer, B., Imposition of local boundary conditions in peridynamics without a fictitious layer and unphysical stress concentrations, Comput. Methods Appl. Mech. Engrg., 393, Article 114734 pp. (2022) · Zbl 1507.74050
[18] Madenci, E.; Barut, A.; Futch, M., Peridynamic differential operator and its applications, Comput. Methods Appl. Mech. Engrg., 304, 408-451 (2016) · Zbl 1425.74043
[19] Madenci, E.; Dorduncu, M.; Barut, A.; Futch, M., Numerical solution of linear and nonlinear partial differential equations using the peridynamic differential operator, Numer. Methods Partial Differential Equations, 33, 1726-1753 (2017) · Zbl 1375.65124
[20] Madenci, E.; Barut, A.; Dorduncu, M., Peridynamic Differential Operator for Numerical Analysis (2019), Springer International Publishing · Zbl 07658003
[21] Madenci, E.; Dorduncu, M.; Gu, X., Peridynamic least squares minimization, Comput. Methods Appl. Mech. Engrg., 348, 846-874 (2019) · Zbl 1440.74477
[22] Rabczuk, T.; Ren, H.; Zhuang, X., A nonlocal operator method for partial differential equations with applications to electromagnetic waveguide problem, Comput. Materials Continua (CMC), 59, 1, 31-55 (2019)
[23] Ren, H.; Zhuang, X.; Rabczuk, T., A nonlocal operator method for solving partial differential equations, Comput. Methods Appl. Mech. Eng., 358, Article 112621 pp. (2020) · Zbl 1441.35250
[24] Zhang, Y.; Madenci, E., 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. (2021)
[25] Zhang, Y.; Madenci, E.; Zhang, Q., ANSYS implementation of a coupled 3D peridynamic and finite element analysis for crack propagation under quasi-static loading, Eng. Fract. Mech., 260, Article 108179 pp. (2022)
[26] Ni, T.; Zaccariotto, M.; Zhu, Q. Z.; Galvanetto, U., Static solution of crack propagation problems in peridynamics, Comput. Methods Appl. Mech. Engrg., 346, 126-151 (2019) · Zbl 1440.74034
[27] Kilic, B.; Madenci, E., An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory, Theor. Appl. Fract. Mech., 53, 194-204 (2010)
[28] Gu, X.; Zhang, Q.; Madenci, E.; Xia, X., Possible causes of numerical oscillations in non-ordinary state-based peridynamics and a bond-associated higher-order stabilized model, Comput. Methods Appl. Mech. Engrg., 357, Article 112592 pp. (2019) · Zbl 1442.74031
[29] Madenci, E.; Barut, A.; Phan, N., Bond-based peridynamics with stretch and rotation kinematics for opening and shearing modes of fracture, J. Peridyn. Nonlocal Model., 1-44 (2021)
[30] T.L. Anderson, Fracture Mechanics: Fundamentals and Applications. 3rd ed., Boca Raton, 2017. · Zbl 1360.74001
[31] Silling, S. A.; Askari, E., A meshfree method based on the peridynamic model of solid mechanics, Comput. Struct., 83, 1526-1535 (2005)
[32] Diyaroglu, C.; Madenci, E.; Phan, N., Peridynamic homogenization of microstructures with orthotropic constituents in a finite element framework, Compos. Struct., 227, Article 111334 pp. (2019)
[33] ANSYS.2 Mechanical User’s Guide (2017)
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