A Taylor–Galerkin algorithm for shock wave propagation and strain localization failure of viscoplastic continua

Abstract

This paper presents a Taylor–Galerkin algorithm formulated in terms of velocities and stresses which can be applied to solid dynamics problems requiring good resolution of small wavelengths, such as propagation of shocks. The proposed model is both fast, as it uses simple linear elements (triangles in 2D and tetrahedra in 3D), and accurate. It mitigates locking and mesh alignment problems, and therefore can be applied to localized failure computations without the limitations exhibited by the classical displacement formulations.