Mathematics

Dynamic evolution of crack propagation is still an open mathematical problem. I present a one-dimensional model of a dynamic peeling test for a thin film where the wave equation is coupled with  Griffith's criterion for the propagation of the debonding front. This simplified problem presents  the main difficulties of the general one, since the domain for the wave equation depends on time.  We have existence and uniqueness for the solution to the coupled problem under different assumptions on the data. Moreover, the study of the asymptotic case, as the loading speed tends to zero, shows that the convergence to a quasistatic equilibrium is not in general satisfied because Griffith's criterion is not satisfied in the limit.