Fracture with healing: A first step towards a new view of cavitation

Recent experimental evidence on rubber has revealed that the internal cracks that arise out of the process, often referred to as cavitation, can actually heal. We demonstrate that crack healing can be incorporated into the variational framework for quasistatic brittle fracture evolution that has been developed in the last twenty years. This will be achieved for two-dimensional linearized elasticity in a topological setting, that is, when the putative cracks are closed sets with a preset maximum number of connected components. Other important features of cavitation in rubber, such as near incompressibility and the evolution of the fracture toughness as a function of the cumulative history of fracture and healing, have yet to be addressed even in the proposed topological setting.