A Formulation of Anisotropic Elastic Damage Using Compact Tensor Formalism

Abstract

An anisotropic elastic-damage model for initially-isotropic materials is presented. The model is based on a pseudo-logarithmic second-order damage tensor rate. To derive the complete expression of the tangent stiffness entering the rate constitutive law, various tensor operations and derivatives of tensor functions must be developed. Such derivations have been performed in compact form. Some useful tensor derivatives and a table of tensor algebra operations are given in Appendix. This note should interest engineering researchers involved in the development of constitutive models through tensor formalism.