Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Abstract

Simulation of generalized fracture and fragmentation remains an ongoing challenge in computational fracture mechanics. There are difficulties associated not only with the formulation of physically based models of material failure, but also with the numerical methods required to treat geometries that change in time. The issue of fracture criteria is addressed in this work through a cohesive view of materials, meaning that a finite material strength and work to fracture are included in the material description. In this study, both surface and bulk cohesive formulations are presented for modeling brittle fracture, detailing the derivation of the formulations, fitting relations, and providing a critical assessment of their capabilities in numerical simulations of fracture. Due to their inherent adaptivity and robustness under severe deformation, meshfree methods are especially well suited to modeling fracture behavior. Described are the applications of meshfree methods to both bulk and surface approaches to cohesive modeling. Numerical examples are provided to highlight the capabilities and shortcomings of the methods in order to identify which approaches are best suited to modeling different types of fracture phenomena.