Author(s)

P. Berest, Q.S. Nguyen & R.M. Pradeilles-Duval

Abstract

Stability and bifurcation of plane cracks of arbitrary shape P. Berest, Q.S. Nguyen, R.M. Pradeilles-Duval Laboratoire de Mecanique des Solides, Ecole Poly technique, 91128 Palaiseau, France ABSTRACT The extension of a plane crack of arbitrary shape in an elastic solid is discussed for G-based laws of propagation. It is shown that the rate of extension is governed by a variational inequality in which the second derivative of the potential energy and of the dissipated energy play a fundamental role. Crack surface is the principal unknown, the differentiation of energy must be performed with respect to a variable domain with moving boundary. Bifurcation and stability of the crack front curve can be discussed as in plasticity. The obtained results are illustrated by some simple analytical exam- ples. INTRODUCTION The propagation of plane cracks of arbitrary shape is an interesting problem in fatigue or in fracture analysis. For example, the study of a plane crack of delamination p

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