Explicit multistep time integration for discontinuous elastic stress wave propagation in heterogeneous solids

Abstract

SummaryA multistep explicit time integration algorithm is presented for tracking the propagation of discontinuous stress waves in heterogeneous solids whose subdomain‐to‐subdomain critical time step ratios range from tens to thousands. The present multistep algorithm offers efficient and accurate computations for tracking discontinuous waves propagating through such heterogeneous solids. The present algorithm, first, employs the partitioned formulation for representing each subdomain, whose interface compatibility is enforced via the method of the localized Lagrange multipliers. Second, for each subdomain, the governing equations of motion are decomposed into the extensional and shear components so that tracking of waves of different propagation speeds is treated with different critical step sizes to significantly reduce the computational dispersion errors. Stability and accuracy analysis of the present multistep time integration is performed with one‐dimensional heterogeneous bar. Analyses of the present algorithm are also demonstrated as applied to the stress wave propagation in one‐dimensional heterogeneous bar and in heterogeneous plain strain problems.