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.