Tensor formalism in the formulation of elastic degradation and damage

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 form of the tangent stiffness, 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 the Appendices. This note should interest engineering researchers involved in the development of constitutive models through tensor formalism.