Constitutive relations of orthotropic elastic damage with dual properties

A phenomenological constitutive framework of orthotropic elastic damage in initially-isotropic materials is presented. Focus is made on secant stress/strain relations that are derived through the application of the so-called damage-effect tensors, namely the fourth-order operators that define the linear transformations between nominal and effective stress and strain quantities. In the attempt to provide selected forms of anisotropic damage approaching general orthotropy, several proposals of damage-effect tensors are formulated. Such fourth-order operators are obtained from the general orthotropic representations as particular instances that satisfy a specific duality requirement between compliance- and stiffness-based derivations.