A concurrent two-scale coupling for wave propagation using direct solution schemes with explicit time integration

Abstract

This article proposes an efficient concurrent coupling of two different material scales—a macroscale and a microscale—in a direct solution scheme based on explicit time integration. Both scales may be discretized with different element sizes and the microdomain may exhibit a heterogeneous structure. A surface coupling is described, which imposes the macrovelocities at the interfaces on the microscale. Using an averaged stress state of several elements on the microscale within a bounded volume, forces are derived which transfer the micromaterial response back to the macroscale. Whereas established surface couplings based on Lagrange multipliers achieve an exact solution of the interface problem, the proposed coupling is based on a weak staggered scheme. The advantage is that no common global system of equations has to be solved and the approach preserves the efficiency of direct solution schemes almost completely. It is therefore well applicable to the simulation of wave propagation phenomena in heterogeneous materials with complex constitutive models and suitable for massive parallelization. Example simulations demonstrate the capabilities and current limitations.