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 const itutive equations of engineering materials at a slow pace. One of the main reasons is the difficulty of establishing general evolution laws. This orig inates from the lack of physical meaning of the thermodynamic forces conjug ate to the damage variables, which finally constitute the space in which lo ading functions and 'damage rules' are defined. In this article, the author s propose a new 'pseudo-logarithmic' rate of damage, which has the advantag e of exhibiting a simple and meaningful conjugate force with very convenien t properties. A main advantage is the physical interpretation of the corres ponding "damage rule", which clearly separates the effects of its volumetri c part, responsible for isotropic degradation, from its deviatoric part, re sponsible for anisotropic effects. This new concept is applied to a second- order tensor secant formulation, which is developed using traditional conce pts 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 'ge neralized pseudo-Rankine' model, is presented and verified with analytical and numerical examples in a companion 'Part II' paper. (C) 2000 Elsevier Sc ience Ltd. All rights reserved.