An Introduction to the LS-DYNA Smoothed Particle Galerkin Method for Severe Deformation and Failure Analyses in Solids

This paper presents a new particle method in LS-DYNA for the severe deformation and failure analyses of solid mechanics problems. The new formulation is first established following a standard meshfree Galerkin approach for a solving of the partial differential equation of linear elastic problems. A smoothed displacement field is introduced to the Galerkin formulation and leads to a regularized smoothed strain approximation. The resultant smoothed/regularized strain formulation can be related to the residual-based stabilization method for the elimination of zeroenergy modes in the conventional particle methods. The discretized system of equations are consistently derived within the meshfree Galerkin variational framework and integrated using a direct nodal integration scheme. The linear formulation is next extended to the large deformation and failure analyses of inelastic materials. In the severe deformation range, an adaptive Lagrangian or Eulerian kernel approach can be preformed to reset the reference configuration and maintain the injective deformation mapping at the particles. Several numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed method.