Calculus of Variations and Geometric Measure Theory

G. A. Francfort - A. Giacomini - O. Lopez-Pamies

A first step towards a variational view of cavitation

created by giacomini on 12 Jan 2018


Submitted Paper

Inserted: 12 jan 2018
Last Updated: 12 jan 2018

Year: 2017


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.

In this contribution we demonstrate that crack healing can be incorporated into the variational framework for quasi-static 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.

Keywords: free discontinuity problems, fracture, minimizing evolutions