On an Eigendeformation Approach to Brittle Fracture

The paper presents a numerical implementation of a novel approximation scheme for Griffith’s theory of brittle fracture recently proposed in [1]. The total potential energy of a brittle body (including bulk and surface terms) is variationally approximated by a family of functionals, depending on a small penalty parameter ε. The (two-field) approximating functionals have as arguments the displacement field u and an eigendeformation field γ. The latter describes the regions of the body under high strains, where fracture will occur. Γ-convergence of such a family of functionals to Griffith’s energy has been proved in [1]. Here we investigate numerical examples for the quasi-static crack propagation in mixed modes I-II and I-III, through finite element approximation, illustrating the main computational features of the eigenfracture approach.