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