On structural computations until fracture based on an anisotropic and unilateral damage theory

This paper describes the formulation and numerical implementation of a family of anisotropic and unilateral damage models for the prediction of damage and final rupture in engineering structures. The damage can be load oriented, microstructure oriented, or (for the first time within this modeling framework) softening. The local equations are solved using a combination of fixed-point and Newton-Raphson algorithms, whose efficiencies are drastically improved through Aitken's relaxation and BFGS approximation. A delay-effect method is used to control the localization of damage, which leads to an objective calculation of the final rupture of structures.