Calculus of Variations and Geometric Measure Theory

M. Negri

From rate-dependent to rate-independent brittle crack propagation

created by negri on 21 Apr 2009
modified on 10 Mar 2010


Published Paper

Inserted: 21 apr 2009
Last Updated: 10 mar 2010

Journal: J. Elast.
Volume: 98
Pages: 159-178
Year: 2010


On the base of many experimental results, e.g. Ravi-Chandar & Knauss (84), Sharon, Gross & Fineberg (96), Hauch & Marder (98), 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.