An artificial viscosity method for the Lagrangian analysis of shocks in solids with strength on unstructured, arbitrary order tetrahedral meshes

Abstract

We present an artificial viscosity scheme tailored to finite-deformation Lagrangian calculations of shocks in materials with or without strength on unstructured tetrahedral meshes of arbitrary order. The artificial viscous stresses are deviatoric and satisfy material-frame indifference exactly. We have assessed the performance of the method on selected tests, including: a two-dimensional shock tube problem on an ideal gas; a two-dimensional piston problem on tantalum without strength; and a three-dimensional plate impact problem on tantalum with strength. In all cases, the artificial viscosity scheme returns stable and ostensibly oscillation-free solutions on meshes which greatly underresolve the actual shock thickness. The scheme typically spreads the shock over 4 to 6 elements and captures accurately the shock velocities and jump conditions.

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