Dynamic fracture based on Griffith's criterion

There has been much recent progress in extending Griffith's criterion for

crack growth into mathematical models for quasi-static crack evolution

that are well-posed, in the sense that there exist solutions that can be

numerically approximated. However, mathematical progress in dynamic

fracture (crack growth consistent with Griffith's criterion, together with

elastodynamics) has been meager. We describe some recent results on a

phase-field model of dynamic fracture, as well as some models based on a

"sharp interface" instead of a phase-field.

Some possible strategies for showing existence for these last models will

also be described.