Local minimality and crack prediction in quasi-static Griffith fracture evolution

Christopher J. Larsen

doi:10.3934/dcdss.2013.6.121

Article Contents

2013, Volume 6, Issue 1: 121-129. Doi: 10.3934/dcdss.2013.6.121

This issue Previous Article The Preisach hysteresis model: Error bounds for numerical identification and inversion Next Article Some remarks on the viscous approximation of crack growth

Local minimality and crack prediction in quasi-static Griffith fracture evolution

Christopher J. Larsen^1,

1.
Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road，Worcester, MA 01609

Received: April 2011

Revised: July 2011

Published: February 2013

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Abstract

The mathematical analysis developed for energy minimizing fracture evolutions has been difficult to extend to locally minimizing evolutions. The reasons for this difficulty are not obvious, and our goal in this paper is to describe in some detail what precisely the issues are and why the previous analysis in fact cannot be extended to the most natural models based on local minimality. We also indicate how the previous methods can be modified for the analysis of models based on a recent definition of stability that is a bit stronger than local minimality.

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Mathematics Subject Classification: Primary: 74R10; Secondary: 49Q20 74G65 74H55.

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