WIAS Preprint No. 1268, (2007)

On the inviscid limit of a model for crack propagation



Authors

  • Knees, Dorothee
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Zanini, Chiara

2010 Mathematics Subject Classification

  • 49J40 74R10 49L25 35K90 74B20 74G65

Keywords

  • rate-indepentent problems, energetic formulation, energy release rate, Griffith fracture criterion, vanishing viscosity method

Abstract

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 Francfort/Marigo model). We construct solutions to the local model via the vanishing viscosity method and compare different notions of weak, local and global solutions.

Appeared in

  • Math. Models Methods Appl. Sci., 18 (2008) pp. 1529--1569.

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