A High-Order Eulerian Godunov Method for Elastic–Plastic Flow in Solids

We present an explicit second-order-accurate Godunov finite difference method for the solution of the equations of solid mechanics in one, two, and three spatial dimensions. The solid mechanics equations are solved in nonconservation form, with the novel application of a diffusion-like correction to enforce the gauge condition that the deformation tensor be the gradient of a vector. Physically conserved flow variables (e.g., mass, momentum, and energy) are strictly conserved; only the deformation gradient field is not. Verification examples demonstrate the accurate capturing of plastic and elastic shock waves across approximately five computational cells. 2D and 3D results are obtained without spatial operator splitting.