On the formulation of anisotropic elastic degradation. I. Theory based on a pseudo-logarithmic damage tensor rate

In spite of its appeal, anisotropic damage is being introduced in the constitutive equations of engineering materials at a slow pace. One of the main reasons is the difficulty of establishing general evolution laws. This originates from the lack of physical meaning of the thermodynamic forces conjugate to the damage variables, which finally constitute the space in which loading functions and 'damage rules' are defined. In this article, the authors propose a new 'pseudo-logarithmic' rate of damage, which has the advantage of exhibiting a simple and meaningful conjugate force with very convenient properties. A main advantage is the physical interpretation of the corresponding "damage rule", which clearly separates the effects of its volumetric part, responsible for isotropic degradation, from its deviatoric part, responsible for anisotropic effects. This new concept is applied to a second-order tensor secant formulation, which is developed using traditional concepts of continuum damage mechanics within the general theoretical framework of elastic degradation and damage recently proposed by the authors. A first example of anisotropic damage formulation based on these concepts, the 'generalized pseudo-Rankine' model, is presented and verified with analytical and numerical examples in a companion 'Part II' paper.