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 diculty of establishing general evolution laws. This originates from the lack of physical meaning of the thermodynamic forces conjugate to the damage variables, which ®nally constitute the space in which loading functions and `damage rulesʹ are de®ned. In this article, the authors propose a new `pseudologarithmicʹ 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 ruleʹʹ, which clearly separates the e€ects of its volumetric part, responsible for isotropic degradation, from its deviatoric part, responsible for anisotropic e€ects. 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 ®rst example of anisotropic damage formulation based on these concepts, the `generalized pseudo-Rankineʹ model, is presented and veri®ed with analytical and numerical examples in a companion `Part IIʹ paper