A new diffuse interface approach to brittle fracture

We present a continuum model for the propagation of cracks and fractures in brittle materials where {\it the full set of variables are the components of the strain tensor $\varepsilon$}. The evolution equations are based on a free energy that reduces to that of linear elasticity for small $\varepsilon$, and accounts for cracks through energy saturation at large values of $\varepsilon$. We regularize the model including terms dependent on gradients of $\varepsilon$ 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 criterion. In addition, regularization makes the results insensitive to the numerical mesh used, something not at all trivial in crack modeling. This new technique presents a broad spectrum of possibilities. We will show a non trivial applications for quasistatic crack propagation in $2D$, the prediction of the growth and curving of cracks. The model could be used to study the dynamics of cracks, as sound emission, cracks instabilities and bifurcation, and it also could be extended to study problems in 3D.