A Numerical Study of a Fully Conservative Method for Hyperelastic-viscoplastic Materials

We present a numerical algorithm for the simulation of the impact of hyperelastic-viscoplastic materials in two dimensions. There are several distinctive aspects of our approach. The governing equations are based on a fully conservative Eulerian formulation due to Plohr and Sharp and our modiication of the Steinberg-Lund rate dependent plasticity model. An approximate 2D Riemann solver is constructed in a directionally unsplit manner to resolve the complex elasto-plastic wave structure. The front tracking method provides sharp resolution of interfaces in multi-material problems while eliminating spurious numerical diiusion and the need for mixed material cell constitutive models. Several example problems are presented as a test of our algorithm. 1. Introduction The numerical modeling of large deformation elasto-plastic materials is challenging because the physics is highly nonlinear, leading to complicated wave patterns and ultimately to material fracture and fragmentation. Impact problems in particular involve material boundaries and shock waves as dis-continuous solution features. In more than one-dimension the characteristic structure of the equations and the wave structure of the solutions are quite complex. Traditionally, numerical computations for such problems are based on La-grangian methods, and are not fully conservative owing to the use of stress variables to represent material states. Mesh distortion limits the Lagrangian formulation to problems with small to moderate deformations. Lagrangian remeshing degrades the accuracy of shock propagation and causes numerical diiusion. Standard multi-material Eulerian methods (one or more Lagrangian