Bifurcation Effects in Ductile Metals With Nonlocal Damage

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.