Anisotropic Damage Effect Tensors for the Symmetrization of the Effective Stress Tensor

[+] Author and Article Information
G. Z. Voyiadjis, T. Park

Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803

J. Appl. Mech 64(1), 106-110 (Mar 01, 1997) (5 pages) doi:10.1115/1.2787259 History: Received August 31, 1995; Revised May 24, 1996; Online October 25, 2007


Based on the concept of the effective stress and on the description of anisotropic damage deformation within the framework of continuum damage mechanics, a fourth order damage effective tensor is properly defined. For a general state of deformation and damage, it is seen that the effective stress tensor is usually asymmetric. Its symmetrization is necessary for a continuum theory to be valid in the classical sense. In order to transform the current stress tensor to a symmetric effective stress tensor, a fourth order damage effect tensor should be defined such that it follows the rules of tensor algebra and maintains a physical description of damage. Moreover, an explicit expression of the damage effect tensor is of particular importance in order to obtain the constitutive relation in the damaged material. The damage effect tensor in this work is explicitly characterized in terms of a kinematic measure of damage through a second-order damage tensor. In this work, tensorial forms are used for the derivation of such a linear transformation tensor which is then converted to a matrix form.

Copyright © 1997 by The American Society of Mechanical Engineers
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