Crack propagation by a regularization of the principle of local symmetry

Matteo Negri

doi:10.3934/dcdss.2013.6.147

Article Contents

2013, Volume 6, Issue 1: 147-165. Doi: 10.3934/dcdss.2013.6.147

This issue Previous Article Some remarks on the viscous approximation of crack growth Next Article A characterization of energetic and $BV$ solutions to one-dimensional rate-independent systems

Crack propagation by a regularization of the principle of local symmetry

Matteo Negri^1,

1.
Dipartimento di Matematica, Università degli Studi di Pavia, Via A. Ferrata 1 - 27100 Pavia

Received: March 31, 2011

Revised: November 30, 2011

Published: January 2013

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Abstract

For planar mixed mode crack propagation in brittle materials many similar criteria have been proposed. In this work the Principle of Local Symmetry together with Griffith Criterion will be the governing equations for the evolution. The Stress Intensity Factors, a crucial ingredient in the theory, will be employed in a 'non-local' (regularized) fashion. We prove existence of a Lipschitz path that satisfies the Principle of Local Symmetry (for the approximated stress intensity factors) and then existence of a $BV$-parametrization that satisfies Griffith Criterion (again for the approximated stress intensity factors).

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Mathematics Subject Classification: Primary: 74R10; Secondary: 74A45.

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