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RESEARCH PAPERS

Bifurcation Effects in Ductile Metals With Nonlocal Damage

[+] Author and Article Information
J. B. Leblond

Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie, Tour 66, 4 place Jussieu, 75005 Paris, France

G. Perrin

Laboratoire de Mécanique des Solides, Ecole Polytechnique, 91128 Palaiseau, France

J. Devaux

FRAMASOFT + CSI, 10 rue Juliette Récamier, 69398 Lyon Cedex 03, France

J. Appl. Mech 61(2), 236-242 (Jun 01, 1994) (7 pages) doi:10.1115/1.2901435 History: Received January 31, 1991; Revised April 16, 1993; Online March 31, 2008

Abstract

The purpose of this paper is to investigate some bifurcation phenomena in a porous ductile material described by the classical Gurson (1977) model, but with a modified, nonlocal evolution equation for the porosity. Two distinct problems are analyzed theoretically: appearance of a discontinuous velocity gradient in a finite, inhomogeneous body, and arbitrary loss of uniqueness of the velocity field in an infinite, homogeneous medium. It is shown that no bifurcation of the first type can occur provided that the hardening slope of the sound (void-free) matrix is positive. In contrast, bifurcations of the second type are possible; nonlocality does not modify the conditions of first occurrence of bifurcation but does change the corresponding bifurcation mode, the wavelength of the latter being no longer arbitrary but necessarily infinite. A FE study of shear banding in a rectangular mesh deformed in plane strain tension is finally presented in order to qualitatively illustrate the effect of finiteness of the body; numerical results do evidence notable differences with respect to the case of an infinite, homogeneous medium envisaged theoretically.

Copyright © 1994 by The American Society of Mechanical Engineers
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