A new generalized finite element method for two-scale simulations of propagating cohesive fractures in 3-D

This paper presents a novel numerical framework based on the generalized finite element method with global-local enrichments (GFEM^gl) for two-scale simulations of propagating fractures in three dimensions. A non-linear cohesive law is adopted to capture objectively the dissipated energy during the process of material degradation without the need of adaptive remeshing at the macro scale or artificial regularization parameters. The cohesive crack is capable of propagating through the interior of finite elements in virtue of the partition of unity concept provided by the generalized/extended finite element method, and thus eliminating the need of interfacial surface elements to represent the geometry of discontinuities and the requirement of finite element meshes fitting the cohesive crack surface. The proposed method employs fine-scale solutions of non-linear local boundary-value problems extracted from the original global problem in order to not only construct scale-bridging enrichment functions but also to identify damaged states in the global problem, thus enabling accurate global solutions on coarse meshes. This is in contrast with the available GFEM^gl in which the local solution field contributes only to the kinematic description of global solutions. The robustness, efficiency, and accuracy of this approach are demonstrated by results obtained from representative numerical examples.