Numerical investigation of dynamic brittle fracture via gradient damage models

Abstract

Gradient damage models can be acknowledged as a unified framework of dynamic brittle fracture. As a phase-field approach to fracture, they are gaining popularity over the last few years in the computational mechanics community. This paper concentrates on a better understanding of these models. We will highlight their properties during the initiation and propagation phases of defect evolution. The variational ingredients of the dynamic gradient damage model are recalled. Temporal discretization based on the Newmark- $$\beta $$ scheme is performed. Several energy release rates in gradient damage models are introduced to bridge the link from damage to fracture. An antiplane tearing numerical experiment is considered. It is found that the phase-field crack tip is governed by the asymptotic Griffith’s law. In the absence of unstable crack propagation, the dynamic gradient damage model converges to the quasi-static one. The defect evolution is in quantitative accordance with the linear elastic fracture mechanics predictions. These numerical experiments provide a justification of the dynamic gradient damage model along with its current implementation, when it is used as a phase-field model for complex real-world dynamic fracture problems.