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

In the companion 'Part I' article, the theoretical aspects of anisotropic d amage based on second-order tensors were discussed, and the concept of pseu do-logarithmic rate of damage was introduced. The thermodynamic forces conj ugate to this damage rate exhibit physical meaning, which greatly simplifie s 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 i n pseudo-log space may assume shapes which vary gradually between a pi -pla ne and a Rankine-type criterion. This corresponds to a transition from a pu rely isotropic to a highly anisotropic tensile degradation model. In spite of the relative complexity of anisotropy, one of the important advantages o f the model is that closed-form solutions are possible for a number of simp le 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 sigma (t) and fracture energy per unit volume g(f). Ad ding the two isotropic elastic constants, this makes a total of only five m aterial parameters. Additional closed-form solutions are developed for the simple loading cases of pure shear, pure distortion, and uniaxial tension a fter tensile loading-unloading in a perpendicular direction. The behavior o f the new model under complex loading histories is illustrated with a numer ical tension/shear test with a significant rotation of principal strains. ( C) 2000 Elsevier Science Ltd. All rights reserved.