Multi-adaptive coupling of finite element meshes with peridynamic grids: robust implementation and potential applications (original) (raw)
Alhadeff A, Leon SE, Celes W, Paulino GH (2016) Massively parallel adaptive mesh refinement and coarsening for dynamic fracture simulations. Eng Comput 32(3):533–552 Google Scholar
Ballarini R, Diana V, Biolzi L, Casolo S (2018) Bond-based peridynamic modelling of singular and nonsingular crack-tip fields. Meccanica 53(14):3495–3515 MathSciNet Google Scholar
Bazazzadeh S, Mossaiby F, Shojaei A (2020) An adaptive thermo-mechanical peridynamic model for fracture analysis in ceramics. Eng Fract Mech 223:106708 Google Scholar
Behzadinasab M, Foster JT (2019) The third sandia fracture challenge: peridynamic blind prediction of ductile fracture characterization in additively manufactured metal. Int J Fract 218(1–2):97–109 Google Scholar
Belinha J, Azevedo J, Dinis LMDJS, Jorge RN (2018) Simulating fracture propagation in brittle materials using a meshless approach. Eng Comput 34(3):503–522 Google Scholar
Bie Y, Cui X, Li Z (2018) A coupling approach of state-based peridynamics with node-based smoothed finite element method. Comput Methods Appl Mech Eng 331:675–700 MathSciNetMATH Google Scholar
Bobaru F, Zhang G (2015) Why do cracks branch? A peridynamic investigation of dynamic brittle fracture. Int J Fract 196(1–2):59–98 Google Scholar
Bobaru F, Yang M, Alves LF, Silling SA, Askari E, Xu J (2009) Convergence, adaptive refinement, and scaling in 1D peridynamics. Int J Numer Meth Eng 77(6):852–877 MATH Google Scholar
Bobaru F, Foster J, Geubelle P, Silling S (2016) Handbook of peridynamic modeling. Advances in applied mathematics. CRC Press, Boca Raton MATH Google Scholar
Boroomand B, Mossaiby F (2006) Dynamic solution of unbounded domains using finite element method: discrete Green’s functions in frequency domain. Int J Numer Meth Eng 67(11):1491–1530 MathSciNetMATH Google Scholar
Boys B, Dodwell T, Hobbs M, Girolami M (2021) PeriPy—a high performance OpenCL peridynamics package. Comput Methods Appl Mech Eng 386:114085 MathSciNetMATH Google Scholar
Brothers MD, Foster JT, Millwater HR (2014) A comparison of different methods for calculating tangent-stiffness matrices in a massively parallel computational peridynamics code. Comput Methods Appl Mech Eng 279:247–267 MATH Google Scholar
Diana V, Carvelli V (2020) An electromechanical micropolar peridynamic model. Comput Methods Appl Mech Eng 365:112998 MathSciNetMATH Google Scholar
Diehl P, Jha P.K., Kaiser H, Lipton R, Levesque M (2018) Implementation of Peridynamics utilizing HPX—the C++ standard library for parallelism and concurrency. arXiv pp. arXiv–1806
Diehl P, Prudhomme S, Lévesque M (2019) A review of benchmark experiments for the validation of peridynamics models. J Peridynam Nonlocal Model 1(1):14–35 MathSciNet Google Scholar
Dipasquale D, Zaccariotto M, Galvanetto U (2014) Crack propagation with adaptive grid refinement in 2D peridynamics. Int J Fract 190(1–2):1–22 Google Scholar
Dipasquale D, Sarego G, Zaccariotto M, Galvanetto U (2016) Dependence of crack paths on the orientation of regular 2D peridynamic grids. Eng Fract Mech 160:248–263 Google Scholar
Dipasquale D, Sarego G, Prapamonthon P, Yooyen S, Shojaei A (2022) A stress tensor-based failure criterion for ordinary state-based peridynamic models. J Appl Comput Mech 8:617–628 Google Scholar
Diyaroglu C, Oterkus E, Oterkus S, Madenci E (2015) Peridynamics for bending of beams and plates with transverse shear deformation. Int J Solids Struct 69:152–168 Google Scholar
Du Q, Han H, Zhang J, Zheng C (2018) Numerical solution of a two-dimensional nonlocal wave equation on unbounded domains. SIAM J Sci Comput 40(3):A1430–A1445 MathSciNetMATH Google Scholar
Elices M, Guinea G, Gomez J, Planas J (2002) The cohesive zone model: advantages, limitations and challenges. Eng Fract Mech 69(2):137–163 Google Scholar
Engquist B, Majda A (1977) Absorbing boundary conditions for numerical simulation of waves. Proc Natl Acad Sci 74(5):1765–1766 MathSciNetMATH Google Scholar
Fan H, Li S (2017) Parallel peridynamics-SPH simulation of explosion induced soil fragmentation by using OpenMP. Comput Particle Mech 4(2):199–211 Google Scholar
Galvanetto U, Mudric T, Shojaei A, Zaccariotto M (2016) An effective way to couple FEM meshes and Peridynamics grids for the solution of static equilibrium problems. Mech Res Commun 76:41–47 Google Scholar
Gao W, Chen X, Wang X, Hu C (2020) Novel strength reduction numerical method to analyse the stability of a fractured rock slope from mesoscale failure. Eng Comput:1–17
Gu X, Zhang Q, Xia X (2017) Voronoi-based peridynamics and cracking analysis with adaptive refinement. Int J Numer Meth Eng 112(13):2087–2109 MathSciNet Google Scholar
Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162(1–2):229–244 MATH Google Scholar
Han F, Lubineau G, Azdoud Y, Askari A (2016) A morphing approach to couple state-based peridynamics with classical continuum mechanics. Comput Methods Appl Mech Eng 301:336–358 MathSciNetMATH Google Scholar
Hermann A, Shojaei A, Steglich D, Höche D, Zeller-Plumhoff B, Cyron CJ (2022) Combining peridynamic and finite element simulations to capture the corrosion of degradable bone implants and to predict their residual strength. Int J Mech Sci 220:107143 Google Scholar
Higdon RL (1991) Absorbing boundary conditions for elastic waves. Geophysics 56(2):231–241 Google Scholar
Lages EN, Paulino GH, Menezes IF, Silva RR (1999) Nonlinear finite element analysis using an object-oriented philosophy-application to beam elements and to the cosserat continuum. Eng Comput 15(1):73–89 Google Scholar
Le Q, Bobaru F (2018) Surface corrections for peridynamic models in elasticity and fracture. Comput Mech 61(4):499–518 MathSciNetMATH Google Scholar
Lubineau G, Azdoud Y, Han F, Rey C, Askari A (2012) A morphing strategy to couple non-local to local continuum mechanics. J Mech Phys Solids 60(6):1088–1102 MathSciNet Google Scholar
Madenci E, Dorduncu M, Barut A, Phan N (2018) Weak form of peridynamics for nonlocal essential and natural boundary conditions. Comput Methods Appl Mech Eng 337:598–631 MathSciNetMATH Google Scholar
Mattesi V, Darbas M, Geuzaine C (2019) A high-order absorbing boundary condition for 2D time-harmonic elastodynamic scattering problems. Comput Math Appl 77(6):1703–1721 MathSciNetMATH Google Scholar
Mossaiby F, Shojaei A, Zaccariotto M, Galvanetto U (2017) OpenCL implementation of a high performance 3D Peridynamic model on graphics accelerators. Comput Math Appl 74(8):1856–1870 MathSciNetMATH Google Scholar
Mossaiby F, Shojaei A, Boroomand B, Zaccariotto M, Galvanetto U (2020) Local dirichlet-type absorbing boundary conditions for transient elastic wave propagation problems. Comput Methods Appl Mech Eng 362:112856 MathSciNetMATH Google Scholar
Ni T, Zaccariotto M, Zhu QZ, Galvanetto U (2019) Static solution of crack propagation problems in peridynamics. Comput Methods Appl Mech Eng 346:126–151 MathSciNetMATH Google Scholar
Ozdemir M, Oterkus S, Oterkus E, Amin I, Nguyen CT, Tanaka S, El-Aassar A, Shawky H (2021) Evaluation of dynamic behaviour of porous media including micro-cracks by ordinary state-based peridynamics. Eng Comput. https://doi.org/10.1007/s00366-021-01506-4 Article Google Scholar
Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Meth Eng 61(13):2316–2343 MATH Google Scholar
Rabczuk T, Belytschko T (2007) A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Methods Appl Mech Eng 196(29–30):2777–2799 MathSciNetMATH Google Scholar
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H (2010) A simple and robust three-dimensional cracking-particle method without enrichment. Comput Methods Appl Mech Eng 199(37–40):2437–2455 MATH Google Scholar
Ren H, Zhuang X, Cai Y, Rabczuk T (2016) Dual-horizon peridynamics. Int J Numer Meth Eng 108(12):1451–1476 MathSciNet Google Scholar
Ren H, Zhuang X, Rabczuk T (2017) Dual-horizon peridynamics: a stable solution to varying horizons. Comput Methods Appl Mech Eng 318:762–782 MathSciNetMATH Google Scholar
Ren H, Zhuang X, Rabczuk T (2020) Nonlocal operator method with numerical integration for gradient solid. Comput Struct 233:106235 Google Scholar
Roy P, Pathrikar A, Deepu S, Roy D (2017) Peridynamics damage model through phase field theory. Int J Mech Sci 128:181–193 Google Scholar
Seleson P, Beneddine S, Prudhomme S (2013) A force-based coupling scheme for peridynamics and classical elasticity. Comput Mater Sci 66:34–49 Google Scholar
Shojaei A, Hermann A, Seleson P, Cyron CJ (2020) Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models. Comput Mech 66(4):773–793
Shojaei A, Mudric T, Zaccariotto M, Galvanetto U (2016) A coupled meshless finite point/Peridynamic method for 2D dynamic fracture analysis. Int J Mech Sci 119:419–431 Google Scholar
Shojaei A, Zaccariotto M, Galvanetto U (2017) Coupling of 2D discretized Peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour. Eng Comput
Shojaei A, Mossaiby F, Zaccariotto M, Galvanetto U (2018) An adaptive multi-grid peridynamic method for dynamic fracture analysis. Int J Mech Sci 144:600–617 Google Scholar
Shojaei A, Galvanetto U, Rabczuk T, Jenabi A, Zaccariotto M (2019) A generalized finite difference method based on the peridynamic differential operator for the solution of problems in bounded and unbounded domains. Comput Methods Appl Mech Eng 343:100–126 MathSciNetMATH Google Scholar
Shojaei A, Mossaiby F, Zaccariotto M, Galvanetto U (2019) A local collocation method to construct dirichlet-type absorbing boundary conditions for transient scalar wave propagation problems. Comput Methods Appl Mech Eng 356:629–651 MathSciNetMATH Google Scholar
Shojaei A, Hermann A, Cyron CJ, Seleson P, Silling SA (2022) A hybrid meshfree discretization to improve the numerical performance of peridynamic models. Comput Methods Appl Mech Eng 391:114544 MathSciNetMATH Google Scholar
Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–209 MathSciNetMATH Google Scholar
Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17–18):1526–1535 Google Scholar
Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88(2):151–184 MathSciNetMATH Google Scholar
Silling S, Littlewood D, Seleson P (2015) Variable horizon in a peridynamic medium. J Mech Mater Struct 10(5):591–612 MathSciNet Google Scholar
Sukumar N, Moës N, Moran B, Belytschko T (2000) Extended finite element method for three-dimensional crack modelling. Int J Numer Meth Eng 48(11):1549–1570 MATH Google Scholar
Sun W, Fish J (2019) Superposition-based coupling of peridynamics and finite element method. Comput Mech 64(1):231–248 MathSciNetMATH Google Scholar
Wang L, Chen Y, Xu J, Wang J (2017) Transmitting boundary conditions for 1D peridynamics. Int J Numer Meth Eng 110(4):379–400 MathSciNetMATH Google Scholar
Wang X, Kulkarni SS, Tabarraei A (2019) Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems. Comput Methods Appl Mech Eng 344:251–275 MathSciNetMATH Google Scholar
Wang Y, Zhou X, Zhang T (2019) Size effect of thermal shock crack patterns in ceramics: insights from a nonlocal numerical approach. Mech Mater 137:103133 Google Scholar
Weckner O, Abeyaratne R (2005) The effect of long-range forces on the dynamics of a bar. J Mech Phys Solids 53(3):705–728 MathSciNetMATH Google Scholar
Wildman RA, Gazonas GA (2013) A perfectly matched layer for peridynamics in two dimensions. J Mech Mater Struct 7(8):765–781 Google Scholar
Wildman RA, Gazonas GA (2014) A finite difference-augmented peridynamics method for reducing wave dispersion. Int J Fract 190(1–2):39–52 Google Scholar
Yu Y, Bargos FF, You H, Parks ML, Bittencourt ML, Karniadakis GE (2018) A partitioned coupling framework for peridynamics and classical theory: analysis and simulations. Comput Methods Appl Mech Eng 340:905–931 MathSciNetMATH Google Scholar
Yu K, Xin X, Lease KB (2010) A new method of adaptive integration with error control for bond-based peridynamics. In: Proceedings of the world congress on engineering and computer science, vol 2, pp 1041–1046
Zaccariotto M, Tomasi D, Galvanetto U (2017) An enhanced coupling of PD grids to FE meshes. Mech Res Commun 84:125–135 Google Scholar
Zaccariotto M, Mudric T, Tomasi D, Shojaei A, Galvanetto U (2018) Coupling of FEM meshes with Peridynamic grids. Comput Methods Appl Mech Eng 330:471–497 MathSciNetMATH Google Scholar
Zaccariotto M, Shojaei A, Galvanetto U (2021) Chapter 6—coupling of CCM and PD in a meshless way. In: Oterkus E, Oterkus S, Madenci E (eds) Peridynamic modeling, numerical techniques, and applications. Elsevier series in mechanics of advanced materials, Elsevier, pp 113–138. https://doi.org/10.1016/B978-0-12-820069-8.00014-7
Zhang W, Yang J, Zhang J, Du Q (2017) Artificial boundary conditions for nonlocal heat equations on unbounded domain. Commun Comput Phys 21(1):16–39 MathSciNetMATH Google Scholar