Dynamic fracture based on Griffith's criterion
Abstract
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.