Diffuse interface approach to brittle fracture.

We present a continuum model for the propagation of cracks and fractures in brittle materials. The components of the strain tensor epsilon are the fundamental variables. The evolution equations are based on a free energy that reduces to that of linear elasticity for small epsilon, and accounts for cracks through energy saturation at large values of epsilon. We regularize the model by including terms dependent on gradients of epsilon in the free energy. No additional fields are introduced, and then the whole dynamics is perfectly defined. We show that the model is able to reproduce basic facts in fracture physics, like the Griffith's dependence of the critical stress as a minus one-half power of the crack length. In addition, regularization makes the results insensitive to the numerical mesh used, something not at all trivial in crack modeling. We present an example of the application of the model to predict the growth and curving of cracks in a nontrivial geometrical configuration.