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

• Published in: International journal for numerical methods in engineering 2019-05, Vol.118 (5), p.276-302
• Main Authors: Cho, S. S., Kolman, R., González, J. A., Park, K. C.
• Format: Article
• Language: English
• Subjects: Algorithms; component‐wise partitioned equations of motion; Dimensional analysis; Equations of motion; explicit multistep time integration; heterogeneous solids; Lagrange multiplier; localized Lagrange multipliers; Propagation; Stability analysis; Stress propagation; Stress waves; Time integration; Tracking; Wave propagation
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6027

Summary A 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.