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.
