From rate-dependent to quasi-static brittle crack propagation

On the base of many experimental results, e.g. [18], [19], [21], [12], the object of our analysis is a rate-dependent model for the propagation of a crack in brittle materials. Our goal is a mathematical study of the evolution equation in the geometries of the ’Single Edge Notch Tension’ (SENT) and of the ’Compact Tension’ (ASTM-CT). Besides existence and uniqueness, emphasis is placed on the regularity of the evolution making reference to the ’velocity gap’. The transition to the quasi-static regime of Griffith’s model is obtained by time rescaling, proving convergence of the rescaled evolutions and of their energies. Further, the discontinuities of the quasi-static propagation are characterized in terms of unstable branches of evolution in real time frame. The results are illustrated by a couple of numerical examples in the above mentioned geometries. AMS Subject Classification. 74R10