Recent Advances in Gradient-Based Damage Methods for Cohesive Models of Fracture
Recently, much attention has focused on gradient-based damage and phase-field models for fracture problems. In these methods, sharp fracture surfaces are approximated with a scalar damage field that varies continuously throughout the domain. The evolution of the damage field is determined by a secondary equation that incorporates a length scale for regularization. These models have enabled simulations of complex fracture problems in three dimensions and demonstrated robustness for simulating challenging phenomena such as crack bifurcations and coalescence. Many of these approaches have been based on a variational formulation for Griffith-type fracture models. While these approaches have seen considerable success, they have also suffered from a number of shortcomings. These include, for example, an explicit relationship between the regularization length and the fracture properties, and challenges associated with introducing critical thresholds for the onset of damage. In this talk, we describe an alternative approach that is based on recent work establishing links between gradient damage methods and cohesive-type models of fracture. The approach naturally introduces a threshold for the onset of damage and allows for the fracture properties to remain fixed as the regularization length scale vanishes. We will discuss strategies for enforcing irreversibility in these approaches, modifications for anisotropic failure problems, and methods to transition from continuous to discontinuous representations of the fracture surfaces. Finally, applications of these models to a range of problems in quasi-static and dynamic fracture in quasi-brittle systems will be presented, including fluid-driven fracture and other types of coupled problems.