A continuous–discontinuous localizing gradient damage framework for failure analysis of quasi-brittle materials

Abstract

This article presents a continuous–discontinuous approach that provides a discontinuous character to the quasi-brittle fracture process, modeled in a continuous setting through a micromorphic stress-based localizing gradient damage framework. The discontinuous framework is developed by enhancing the problem fields using discontinuous interpolations in the critically damaged regions exploiting local partition of unity via the eXtended Finite Element Method (XFEM). The proposed approach incorporates an improved spatial nonlocal diffusive behavior in the continuous bulk through an additional microforce balance equation to ensure an improved prediction of the initial phase of the loading process. Level sets are computed to track the discontinuity within the finite element mesh, predicted via evolving micromorphic equivalent strain. Here, the proposed continuous–discontinuous approach combines the advantages of the gradient damage method and the XFEM while exhibiting improved convergence using low-order finite elements during numerical simulations. The enhanced numerical kinematics of the proposed approach successfully eliminates damage spreading during the final failure stages and provides an accurate description of a true discontinuity without using cohesive zone modeling. Various representative structural examples of benchmark tests involving varying loading conditions are investigated to demonstrate the accuracy and robustness of the proposed approach to provide qualitative and quantitative accurate numerical predictions.