Calculus of Variations and Geometric Measure Theory

D. Knees - A. Mielke - C. Zanini

On the inviscid limit of a model for crack propagation

created by zanini on 06 Dec 2007
modified on 09 Oct 2008


Published Paper

Inserted: 6 dec 2007
Last Updated: 9 oct 2008

Journal: Math. Models Methods Appl. Sci.
Volume: 18
Number: 9
Pages: 1529-1569
Year: 2008


We study the evolution of a single crack in an elastic body and assume that the crack path is known in advance. The motion of the crack tip is modeled as a rate-independent process on the basis of Griffith's local energy release rate criterion. According to this criterion, the system may stay in a local minimum before it performs a jump. The goal of this paper is to prove existence of such an evolution and to shed light on the discrepancy between the local energy release rate criterion and models which are based on a global stability criterion (as for example the FrancfortMarigo model). We construct solutions to the local model via the vanishing viscosity method and compare different notions of weak, local and global solutions.