Why Continuum Damage is Nonlocal: Micromechanics Arguments

The paper presents two micromechanics arguments showing that continuum damage caused by microcracking ought to be nonlocal, defined by a spatial integral. Argument I is an analysis of a simplified model in which the microcracks are of such size, density, and arrangement that that they do not interact. The release of stored energy caused by the formation of one microcrack is calculated as a function of the associated relative displacement across the cell, which corresponds to the average strain of the macroscopic continuum. After imposing two homogenizing conditions, it is shown that damage is a nonlocal variable that is a function of the averaged (nonlocal) strain from a certain neighborhood of the given point. Argument II is an analysis of a body with arbitrary interacting cracks. The local damage is proportional to the forces applied on the cracks to replace the stresses before cracking. Crack formation changes the openings of the neighboring cracks, which represents an interaction described by crack influence coefficients. The non‐locality is a consequence of crack interactions, and the weight function for nonlocal spatial integration appears to be related to the influence coefficients.