Nonlocal Damage Theory Based on Micromechanics of Crack Interactions
Publication: Journal of Engineering Mechanics
Volume 120, Issue 3
Abstract
A nonlocal continuum model for strain‐softening damage is derived by micromechanics analysis of a macroscopically nonhomogeneous (nonuniform) system of interacting and growing microcracks, using Kachanov's simplified version of the superposition method. The homogenization is obtained by seeking a continuum field equation whose possible discrete approximation coincides with the matrix equation governing a system of interacting microcracks. The result is a Fredholm integral equation for the unknown nonlocal inelastic stress increments, which involves two spatial integrals. One integral, which ensues from the fact that crack interactions are governed by the average stress over the crack length rather than the crack center stress, represents short‐range averaging of inelastic macro‐stresses. The kernel of the second integral is the long‐range crack influence function which is a second‐rank tensor and varies with directional angle (i.e., is anisotropic), exhibiting sectors of shielding and amplification. For long distances , the weight function decays as in two dimensions and as in three dimensions. Application of the Gauss‐Seidel iteration method, which can conveniently be combined with iterations in each loading step of a nonlinear finite element code, simplifies the handling of the nonlocality by allowing the nonlocal inelastic stress increments to be calculated from the local ones explicitly. This involves evaluation of an integral involving the crack influence function, for which closed‐form expressions are derived. Because the constitutive law is strictly local, no difficulties arise with the unloading criterion or continuity condition of plasticity.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 120 • Issue 3 • March 1994
Pages: 593 - 617
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jul 28, 1992
Published online: Mar 1, 1994
Published in print: Mar 1994
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