Crack Growth Laws from Symmetry
  Reviewing work done in collaboration with Jennifer Hodgdon, we derive the most general crack growth law allowed by symmetry for mixed-mode three-dimensional fracture. We do so using the system developed in condensed matter physics to derive new laws that emerge on long length and time scales. In our derivation, we provide a symmetry interpretation for the three modes of fracture, we rederive the law giving the crack growth direction in two dimensional fracture, and we derive a growth law appropriate for three dimensional simulations. We briefly discuss related work subsequent to ours, incorporating disorder, dynamics, and other internal variables. 
James P. Sethna