Free discontinuity finite element models in two-dimensions for in-plane crack problems

Two different free discontinuity finite element models for studying crack initiation and propagation in 2D elastic problems are presented. Minimization of an energy functional, composed of bulk and surface terms, is adopted to search for the displacement field and the crack pattern. Adaptive triangulations and embedded or r-adaptive discontinuities are employed. Cracks are allowed to nucleate, propagate, and branch. In order to eliminate rank-deficiency and perform local minimization, a vanishing viscosity regularization of the discrete Euler–Lagrange equations is enforced. Converge properties of the proposed models are examined using arguments of the Γ-convergence theory. Numerical results for an in-plane crack kinking problem illustrate the main operational features of the free discontinuity approach.