A relation between a dynamic fracture model and quasi-static evolution
Henrique M. Versieux · ESAIM Mathematical Modelling and Numerical Analysis · 2015
We study the relations between a dynamic model proposed by Bourdin, Larsen and Richardson, and quasi-static fracture evolution.We assume the dynamic model has the boundary displacements of the material as input, and consider time-rescaled solutions of this model associated to a sequence of boundary conditions with speed going to zero.Next, we study whether this rescaled sequence converges to a function satisfying quasi-static fracture evolution.Under some hypotheses and assuming the speed of crack propagation slows down following the deceleration of boundary displacements, our main result shows that (up to a subsequence) the rescaled solutions converge to a quasi-static evolution.