On the formulation of anisotropic elastic degradation.: II. Generalized pseudo-Rankine model for tensile damage

Abstract

In the companion `Part I' article, the theoretical aspects of anisotropic damage based on second-order tensors were discussed, and the concept of pseudo-logarithmic rate of damage was introduced. The thermodynamic forces conjugate to this damage rate exhibit physical meaning, which greatly simplifies the task of defining loading surfaces and evolution laws. In this second part, a formulation for anisotropic tensile damage which takes advantage of those concepts is developed and verified: the `generalized pseudo-Rankine' model. Depending on the value of a single parameter, the loading surface in pseudo-log space may assume shapes which vary gradually between a π-plane and a Rankine-type criterion. This corresponds to a transition from a purely isotropic to a highly anisotropic tensile degradation model. In spite of the relative complexity of anisotropy, one of the important advantages of the model is that closed-form solutions are possible for a number of simple loading cases. The first one developed is uniaxial tension, which makes it possible to interpret the remaining two material parameters in terms of the tensile strength σ t and fracture energy per unit volume g f. Adding the two isotropic elastic constants, this makes a total of only five material parameters. Additional closed-form solutions are developed for the simple loading cases of pure shear, pure distortion, and uniaxial tension after tensile loading–unloading in a perpendicular direction. The behavior of the new model under complex loading histories is illustrated with a numerical tension/shear test with a significant rotation of principal strains.