Secant stress/strain relations of orthotropic elastic damage with dual properties

A constitutive framework of orthotropic elastic damage in initially-isotropic materials is presented. The constitutive equations are developed within the phenomenological approach of Continuum Damage Mechanics. Focus is made on secant stress/strain relations that can be derived by 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 complete orthotropic representations as particular instances that satisfy a duality requirement between compliance- and stiffness-based derivations. A complete family of solutions based on a specific non-singular tensor generator is derived in full invariant form.