An Eigendeformation Approach to Brittle Fracture

A new approximation scheme for Griffith's theory of brittle fracture is presented. The energy functional is approximated by a family of functionals depending on a small parameter and two fields: the displacement field and an eigendeformation describing the fractures that may occur in the body. The eigendeformations allow the displacement field to develop jumps that cost fracture energy depending on the $\epsilon$-neighborhoods of their supports. The mathematical outline of the method is briefly sketched, discussing $\Gamma$-convergence of the eigendeformation functional sequence to Griffith's energy. Numerical examples concerned with benchmark problems of brittle fracture illustrate the main numerical features of the proposed approach.