Numerical simulations are indispensible in many engineering disciplines since they can reduce the number of costly and time-consuming experiments. For the prediction of material and structural failure, damage and fracture models have been developed, which are constantly being further extended to consider more and more effects. State-of-the-art isotropic damage models apply scalar variables to describe damage/degradation of a material. Anisotropic damage models have already been developed for quite a time, but in this research field still pending issues exist. One challenging task concerns the mesh-objective description of anisotropic damage progression in finite element simulations. The present cumulative dissertation consists of three peer-reviewed articles that deal with state-of-the-art isotropic damage as well as anisotropic damage representations. In article 1, an application oriented design study utilizing a local isotropic damage model is presented. The other two articles (article 2 and 3) deal with gradient-extended anisotropic damage, for which a new formulation is established.
