Modeling strong discontinuities in the material point method using a single velocity field

Georgios Moutsanidis1, David Kamensky2, Duan Z. Zhang3, Yuri Bazilevs2, Christopher C. Long3
1Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0085, La Jolla, CA 92093, USA
2School of Engineering, Brown University, 184 Hope Street, Providence, RI 02912, USA
3Fluid Dynamics and Solid Mechanics, T-3, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, United States

Tài liệu tham khảo

Sulsky, 1994, A particle method for history-dependent materials, Comput. Methods Appl. Mech. Engrg., 118, 179, 10.1016/0045-7825(94)90112-0 Bardenhagen, 2000, The material-point method for granular materials, Comput. Methods Appl. Mech. Engrg., 187, 529, 10.1016/S0045-7825(99)00338-2 Harlow, 1964, The particle-in-cell computing method for fluid dynamics, Methods Comput. Phys., 3, 319 Evans, 1957 Sulsky, 1995, Application of a particle-in-cell method to solid mechanics, Comput. Phys. Commun., 87, 236, 10.1016/0010-4655(94)00170-7 Sulsky, 1993, A particle method with large rotations applied to the penetration of history-dependent materials, ASME Appl. Mech. Div.-Publ.-AMD, 171 Sulsky, 1993, The particle-in-cell method as a natural impact algorithm, ASME Appl. Mech. Div.-Publ.-AMD, 180 York, 2000, Fluid–membrane interaction based on the material point method, Internat. J. Numer. Methods Engrg., 48, 901, 10.1002/(SICI)1097-0207(20000630)48:6<901::AID-NME910>3.0.CO;2-T Stomakhin, 2013, A material point method for snow simulation, ACM Trans. Graph., 32, 102, 10.1145/2461912.2461948 Andersen, 2010, Modelling of landslides with the material-point method, Comput. Geosci., 14, 137, 10.1007/s10596-009-9137-y Bardenhagen, 2004, The generalized interpolation material point method, Comput. Model. Eng. Sci., 5, 477 Zhen Chen, Rebecca Brannon, An evaluation of the material point method. SAND Report, SAND2002-0482,(February 2002), 2002. Zhang, 2008, Material point method applied to multiphase flows, J. Comput. Phys., 227, 3159, 10.1016/j.jcp.2007.11.021 Zhang, 2011, Material point method enhanced by modified gradient of shape function, J. Comput. Phys., 230, 6379, 10.1016/j.jcp.2011.04.032 Sadeghirad, 2011, A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations, Internat. J. Numer. Methods Engrg., 86, 1435, 10.1002/nme.3110 Zhang, 2016 Nairn, 2003, Material point method calculations with explicit cracks, Comput. Model. Eng. Sci., 4, 649 Guo, 2006, Three-dimensional dynamic fracture analysis using the material point method, Comput. Model. Eng. Sci., 16, 141 Bardenhagen, 2011, Simulation of dynamic fracture with the material point method using a mixed j-integral and cohesive law approach, Int. J. Fract., 170, 49, 10.1007/s10704-011-9602-1 Homel, 2017, Field-gradient partitioning for fracture and frictional contact in the material point method, Internat. J. Numer. Methods Engrg., 109, 1013, 10.1002/nme.5317 Zhang, 2007, CartaBlanca theory manual: multiphase flow equations and numerical methods, 07 Hager, 2009, Nonlinear complementarity functions for plasticity problems with frictional contact, Comput. Methods Appl. Mech. Engrg., 198, 3411, 10.1016/j.cma.2009.06.021 Gingold, 1977, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Not. Royal Astron. Society, 181, 375, 10.1093/mnras/181.3.375 Monaghan, 1992, Smoothed particle hydrodynamics, Annu. Rev. Astron. Astrophys., 30, 543, 10.1146/annurev.aa.30.090192.002551 Liu, 2010, Smoothed particle hydrodynamics (sph): an overview and recent developments, Arch. Comput. Methods Eng., 17, 25, 10.1007/s11831-010-9040-7 Chen, 2017, Meshfree methods: progress made after 20 years, J. Eng. Mech., 143, 04017001, 10.1061/(ASCE)EM.1943-7889.0001176 Chen, 2001, A stabilized conforming nodal integration for galerkin mesh-free methods, Internat. J. Numer. Methods Engrg., 50, 435, 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A Gan, 2018, Enhancement of the material point method using b-spline basis functions, Internat. J. Numer. Methods Engrg., 113, 411, 10.1002/nme.5620 Springel, 2005, The cosmological simulation code gadget-2, Mon. Not. Royal Astron. Soc., 364, 1105, 10.1111/j.1365-2966.2005.09655.x Kamensky, 2018, A contact formulation based on a volumetric potential: Application to isogeometric simulations of atrioventricular valves, Comput. Methods Appl. Mech. Engrg., 330, 522, 10.1016/j.cma.2017.11.007 Logg, 2012 Hu, 2003, A multi-mesh mpm for simulating the meshing process of spur gears, Comput. Struct., 81, 1991, 10.1016/S0045-7949(03)00260-8 VanderHeyden, 2001, Cartablanca—a pure-java, component-based systems simulation tool for coupled non-linear physics on unstructured grids, 134 Zhang, 2005