A formulation of isotropic and anisotropic damage with evolution laws in pseudo-log space

Anisotropic damage modeling still poses a number of open challenges. One of the most important is how to formulate the evolution laws in a way that is reasonably simple and makes physical sense. The theory tells us that loading function and damage rule are better defined in the space of forces conjugate to the primary damage variable. Choosing the 2nd-order integrity tensor (or any of the related tensors) as such variable, the resulting conjugate force tensor lacks physical meaning, and proposing physically meaningful evolution laws becomes a difficult task. A 2nd-order pseudo-log rate of damage has been recently proposed which remedies this problem and exhibits a number of additional advantages. To develop this idea, a 'basic' secant formulation has been considered in which the degraded stiffness depends on only 5 independent parameters. A first anisotropic model which distinguishes tension and compression has been developed based on these ideas, and has been verified in a complex loading case involving rotation of principal axes. All these recent developments are summarized in this paper. In addition, the extension of the secant stiffness from 5 to 6 independent parameters is finally outlined. This extension encompasses purely volumetric and von Mises isotropic damage, and is formulated in a way that preserves most of the convenient features of the basic formulation.