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.