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 others than the strain tensor $\epsilon$ are introduced, and then the whole dynamics is perfectly defined. We validate the model in controlled cases, and present a couple of non trivial applications. 
V. I. Marconi and E. A. Jagla