Dual orthotropic damage-effect tensors with complementary structures

This paper deals with secant constitutive relations of orthotropic elastic damage based on the so-called damage-effect tensors, namely the fourth-order operators that define the linear transformations between nominal and effective stress and strain quantities. The damage-effect tensors are expressed by orthotropic representations in terms of symmetric second-order damage tensor variables. The paper provides a set of new dual orthotropic damage-effect tensors that possess complementary structures in the dual compliance and stiffness-based derivations. More specifically, each orthotropic damage-effect tensor of the solution set possesses an inverse (its dual counterpart) that displays the structure of the (major) transpose of the tensor obtained by replacing the adopted second-order damage tensor variables with their inverses.