A discrete nonlocal damage mechanics approach

References

• E. Tonti, Why starting from differential equations for computational physics? Comput. Phys., vol. 257, pp. 1260–1290, 2014.
   Google Scholar
• S. Murakami, Mechanical modeling of material damage, Trans. ASME J. Appl. Mech., vol. 55, no. 2, pp. 280–286, 1988.
   Web of Science ®Google Scholar
• J.C. Simo and J.W. Ju, On continuum damage-elastoplasticity at finite strains, Comput. Mech., vol. 5, no. 5, pp. 375–400, 1989.
   Google Scholar
• Z.P. Bazant and M. Jirásek, Nonlocal integral formulations of plasticity and damage: survey of progress, J. Eng. Mech., vol. 128, no. 11, pp. 1119–1149, 2002.
   Web of Science ®Google Scholar
• Z.P. Bazant and G. Pijaudier-Cabot, Nonlocal continuum damage, localization instability and convergence, Trans. ASME J. Appl. Mech., vol. 55, no. 2, pp. 287–293, 1988.
   Web of Science ®Google Scholar
• G. Pijaudier-Cabot and Z.P. Bazant, Nonlocal damage theory, J. Eng. Mech., vol. 113, no. 10, pp. 1512–1533, 1987.
   Web of Science ®Google Scholar
• A.R. Srinivasa and J.N. Reddy, An overview of theories of continuum mechanics with nonlocal elastic response and a general framework for conservative and dissipative systems, Appl. Mech. Rev., vol. 69, no. 3, 2017. DOI: 10.1115/1.4036723
   Web of Science ®Google Scholar
• P. Thamburaja, K. Sarah, A. Srinivasa, and J.N. Reddy, Fracture of viscoelastic materials: FEM implementation of a non-local and rate form-based finite-deformation constitutive theory, Comput. Methods Appl. Mech. Eng., vol. 354, pp. 871–903, 2019. DOI: 10.1016/j.cma.2019.05.032.
   Web of Science ®Google Scholar
• M.L. Falk, A. Needleman, and J.R. Rice, A critical evaluation of cohesive zone models of dynamic fractur, J. Phys. IV France, vol. 11, no. PR5, pp. Pr5-43–Pr5-50, 2001.
   Google Scholar
• T. Belytschko, R. Gracie, and G. Ventura, A review of extended/generalized finite element methods for material modeling, Modell. Simul. Mater. Sci. Eng., vol. 17, no. 4, pp. 043001, 2009.
   Web of Science ®Google Scholar
• M. Bußler et al., Visualization of fracture progression in peridynamics, Comput. Graph., vol. 67, pp. 45–57, 2017.
   Web of Science ®Google Scholar
• J.-Y. Wu, A unified phase-field theory for the mechanics of damage and quasi-brittle failure, J. Mech. Phys. Solids, vol. 103, pp. 72–99, 2017.
   Web of Science ®Google Scholar
• K. Sarah, P. Thamburaja, A. Srinivasa, and J.N. Reddy, Numerical simulations of damage and fracture in viscoelastic solids using a nonlocal fracture criterion, Mech. Adv. Mater. Struct., vol. 27, no. 13, pp. 1085–1097, 2020.
   Web of Science ®Google Scholar
• P. Khodabakhshi, J.N. Reddy, and A. Srinivasa, GraFEA: a graph-based finite element approach for the study of damage and fracture in brittle materials, Meccanica, vol. 51, no. 12, pp. 3129–3147, 2016. DOI: 10.1007/s11012-016-0560-6.
   Web of Science ®Google Scholar
• P. Khodabakhshi, J.N. Reddy, and A. Srinivasa, A nonlocal fracture criterion and its effect on the mesh dependency of GraFEA, Acta Mech., vol. 230, no. 10, pp. 3593–3612, 2019.
   Web of Science ®Google Scholar
• P. Alliez, D. Cohen-Steiner, M. Yvinec, and M. Desbrun, Variational tetrahedral meshing, ACM Trans. Graph., vol. 24, no. 3, pp. 617–625, 2005.
   Web of Science ®Google Scholar
• Q. Du, V. Faber, and M. Gunzburger, Centroidal voronoi tessellations: applications and algorithms, SIAM Rev., vol. 41, no. 4, pp. 637–676, 1999. DOI: 10.1137/S0036144599352836.
   Web of Science ®Google Scholar
• Y. Hu, T. Schneider, B. Wang, D. Zorin, and D. Panozzo, Fast tetrahedral meshing in the wild, ACM Trans. Graph., vol. 39, no. 4, pp. 117: 1–117: 18, 2020.
   Web of Science ®Google Scholar
• P. Mullen, P. Memari, F. de Goes, and M. Desbrun, HOT: Hodge-optimized triangulations, ACM Trans. Graph., vol. 30, no. 4, pp. 1–12, 2011.
   Web of Science ®Google Scholar
• S. Sarkar, M. Nowruzpour, J.N. Reddy, and A.R. Srinivasa, A discrete lagrangian based direct approach to macroscopic modelling, J. Mech. Phys. Solids, vol. 98, pp. 172–180, 2017.
   Web of Science ®Google Scholar
• J.N. Reddy and A. Srinivasa, On the force–displacement characteristics of finite elements for elasticity and related problems, Finite Elem. Anal. Des., vol. 104, pp. 35–40, 2015.
   Web of Science ®Google Scholar
• D.A. Birch and W.R. Young, A master equation for a spatial population model with pair interactions, Theor. Popul. Biol., vol. 70, no. 1, pp. 26–42, 2006. DOI: 10.1016/j.tpb.2005.11.007.
   PubMed Web of Science ®Google Scholar
• M. Doi, Stochastic theory of diffusion-controlled reaction, J. Phys. A: Math. Gen., vol. 9, no. 9, pp. 1479–1495, 1976.
   Google Scholar
• M. Galouei and A. Fakhimi, Size effect, material ductility and shape of fracture process zone in quasi-brittle materials, Comput. Geotech., vol. 65, pp. 126–135, 2015.
   Web of Science ®Google Scholar
• J.H.P. De Vree, W.A.M. Brekelmans, and M.A.J. Van Gils, Comparison of nonlocal approaches in continuum damage mechanics, Comput. Struct., vol. 55, no. 4, pp. 581–588, 1995.
   Web of Science ®Google Scholar