A multiscale cohesive zone model and simulations of fractures

Abstract In this work, a novel multiscale cohesive zone model is proposed, in which the bulk material is modeled as a local quasi-continuum medium that obeys the Cauchy–Born rule while the cohesive force and displacement relations inside the cohesive zone are governed by a coarse grained depletion potential. The interface depletion potential is constructed based on the Derjaguin approximation of nonlocal colloidal interactions. By doing so, the interface constitutive descriptions are made genetically consistent with the bulk constitutive relations that are enriched from underneath atomistic structure. The method provides an effective means to describe properties of material inhomogeneities such as grain boundaries, bi-material interfaces, slip lines, and inclusions, etc. We have developed and implemented the proposed multiscale cohesive zone model in a cohesive finite element weak Galerkin formulation, and we have applied it to simulate dynamic fracture problems in solids. The numerical simulation results have shown that the method has successfully captured the phenomenon of spall fracture during simulations of impacts and penetrations.