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Summary: PHILOSOPHICAL MAGAZINE B, 1998, VOL. 78, NO. 2, 97± 102
Crack dynamics in elastic media
By Mokhtar Adda-Bedia and Martine Ben Amar
Laboratoire de Physique Statistique de l'Ecole Normale Supe rieure, Unite de
Recherche associe e au CNRS 1306, Associe e aux Universite s Paris VI et VII,
24 rue Lhomond, F-75231 Paris Cedex 05, France
Abstract
The classical theory of fracture mechanics states that a crack propagating in
an unbounded body should smoothly accelerate until it reaches the Rayleigh wave
speed. We introduce here a general approach for solving the equation of motion
of the crack tip. We show that the loading conditions and the geometry of the
con® guration do not produce inertial e ects. The equation of motion of a
propagating crack is always a ® rst-order di erential equation.
§1. Introduction
Dynamic fracture experiments (Fineberg et al. 1992, Gross et al. 1993, Gross
1995, Boudet et al. 1996, Sharon et al. 1996) have shown many phenomena which are
now admitted to be related to fundamental physical processes. Concerning the
instabilities of dynamic fractures, it has been observed that, when the crack velocity
v exceeds a critical speed Vc, the acoustic emission from the crack increases (Gross et
al. 1993, Boudet et al. 1996), the velocity oscillations are ampli® ed and a pattern
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