A Multiscale Failure Modeling Framework for Strain Localization in Quasi-Brittle Materials

Abstract

Macroscale mesh sensitivity and RVE size dependence are the two major issues that make the conventional homogenization techniques incapable of modeling the softening behavior of quasi-brittle materials. In this paper, a new continuous–discontinuous multiscale modeling approach to failure is presented. Inspired by the classical crack band model of Bazant and Oh (1983), this approach is built upon an extended computational homogenization (CH) scheme for representing the macroscale crack behavior. During the multiscale computation, once a macroscale material point loses its stability with the XFEM, a new crack segment represented is inserted for which cohesive RVE models using the extended CH and with copied initial states are coupled to crack integration points. In the extended CH, the macroscale strain applied to the boundary of the cohesive RVE model is enriched with a macroscale discontinuity related term regularized with the effective length of the microscale localization band. This helps alleviate the RVE size dependency of the homogenized cohesive response. The weakly periodic BCs that are aligned with the localization direction are employed to minimize spurious boundary effects. Several numerical examples are provided to demonstrate the effectiveness of this framework, with a comparison against direct numerical simulations.