A Combined Particle-element Method for High-velocity Impact Computations

Abstract

This article presents a Combined Particle-Element Method (CPEM) for high-velocity impact computations. It includes a description of the numerical algorithms, and example computations. For this new approach the initial mesh is input as solid finite elements, and then it is put into a meshless-particle structure in the preprocessor. The integration points of the original elements are transformed into massless stress points, and the nodes from the original elements carry the mass and accept forces from the stresses. When the equivalent plastic strain in a stress point is less than a user-specified value (ecrit) a finite-element algorithm (formulated within a particle structure) is used to update the strain rates and strains at the stress point, and to compute forces for the (fixed connectivity) particle nodes. When the equivalent plastic strain in a stress point exceeds ecrit the strain rates are determined from the surrounding neighbor nodes (obtained from a search routine) with a Moving Least Squares (MLS) formulation, and the nodal forces are determined from a weak-form formulation. With this approach there is a simple transition between the element and particle algorithms. The advantages are that the lower-strained particles (stress points) are computed with a fast and accurate finite-element formulation, and the higher-strained particles are computed with a meshless-particle formulation that can handle severe distortions. Furthermore, the meshless-particle algorithm (with MLS strain rates and weak-form forces) is consistent and does not exhibit tensile instabilities. It is also well-suited for conversion of finite elements into variable-connectivity meshless particles because it does not require deletion of elements and addition of particles, as required with the existing conversion algorithms that use the Generalized Particle Algorithm (GPA). Instead it is simply a branch point based on equivalent plastic strain. The basic approach can also be used for the element algorithm only or the particle algorithm only.