A high-order Eulerian Godunov method for elastic-plastic flow in solids

We present an explicit second-order-accurate Godunov finite difference meth od for the solution of the equations of solid mechanics in one, two, and th ree spatial dimensions. The solid mechanics equations are solved in noncons ervation 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 e nergy) are strictly conserved; only the deformation gradient field is not. Verification examples demonstrate the accurate capturing of plastic and ela stic shock waves across approximately five computational cells. 2D and 3D r esults are obtained without spatial operator splitting. (C) 2001 Academic P ress.