Expansion of consistent particle method to solve solid mechanics problems

Abstract

AbstractOriginally developed for solving fluid dynamics problems, a Lagrangian particle method called the consistent particle method (CPM) is expanded to solid mechanics problems in this article. The motions of particles are governed by the mass conservation and dynamics equations which are solved by the second‐order predictor–corrector time stepping scheme. The spatial derivatives of variables required in solving the governing equations and computing strain increments are obtained by Taylor series expansion. Stress components are updated from strain components according to the material constitutive relation. The physical density of material is directly computed without using particle number density. No additional particles are needed for the simulation of boundaries. For boundary surface that is partially loaded, the inverse distance weighting method is applied to deal with the stress singularity problem due to sudden change of stresses. Numerical examples including shock wave propagation and large deformation of footing penetration are presented to demonstrate the capabilities of CPM in solving solid mechanics problems.