Numerical simulation of impulse waves in Cosserat media based on a time‐discontinuous Galerkin finite element method

Abstract

AbstractThe time‐discontinuous Galerkin finite element method (TDGFEM) has advantages in reducing spurious numerical oscillations and capturing discontinuities of solutions in space for high‐frequency dynamical problems. This article extends TDGFEM into Cosserat media to focus on impulse wave propagations, involving rotational wave and effects of microstructures. The Cosserat continuum theory contains additional rotational degrees of freedom, leading to Cosserat compressive (P), shear (S), and rotational (R) waves. Therefore, three Cosserat wave propagations are simulated by TDGFEM under impulse loads in this article. Different orders (P1–P3) of temporal shape functions are presented for Cosserat nodal unknown vectors, leading to different matrix equations for TDGFEM. One‐dimensional numerical results show capacity and efficiency of TDGFEM simulating Cosserat impulse wave propagations. Analyses about time step, mesh density and accuracy of TDGFEM are given in one‐dimensional examples. Results simulated by three methods with artificial damping are compared with those by TDGFEM, which shows a higher efficiency for TDGFEM. Two‐dimensional results present the propagation characteristics of Cosserat impulse P, S, and R waves, and velocities of Cosserat P, S, and R waves are simulated by TDGFEM. The characteristic length and Cosserat shear modulus have a major influence on impulse S and R wave propagations.