Local Discontinuous Galerkin Method for the Impact-Induced Wave in a Slender Cylinder Composed of a Non-Convex Elastic Material

Abstract

In this paper, we present a numerical scheme based on the local discontinuous Galerkin (LDG) method for the wave propagation of phase transition in a slender cylinder by introducing new temporal auxiliary variables. The stability for the LDG scheme is presented. In order to verify the validity of the LDG scheme, we give the errors and accuracy order of a numerical example. Due to the interaction between the dispersion and the material nonlinearity, some interesting wave patterns occur for different pre-strains and impacts, such as the pattern with transformation front and solitary wave and the pattern with rarefaction wave and solitary wave. We also investigate the interaction of the transformation fronts and rarefaction waves, and demonstrate this interesting wave phenomena.