Two Dimensional Analysis of Strain Localization with Nonlocal Continuous Damageby Gilles Pijaudier-Cabot, Universite Paris 6, Cachan, France,
Laurent Bode, Universite Paris 6, Cachan, France,
Abstract: This paper addresses the problem of damage localization from a theoretical stand point with a nonlocal model. Conditions for non uniqueness of the rate equations of equilibrium are derived along with the wave-length of the strain rate and damage fields. We find that the width of the localization zone is enforced by the model and that it is proportional to the characteristic length of the nonlocal continuum. Next, the analytical solution is compared with solutions derived from the differential approximation of the integral equations. It is shown that the conditions of loss of uniqueness of the equations of equilibrium cannot be derived directly from this approximation.
Subject Headings: Failure analysis | Equilibrium | Approximation methods | Two-dimensional analysis | Wave equations | Strain rates
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