Simulation of strain localization with gradient enhanced damage models

The incorporation of higher order strain gradients into the constitutive eq uations of continuum damage mechanics is presented. Thereby, not only scala r-valued isotropic damage models but also anisotropic damage models allowin g for directional dependent stiffness degradation are elaborated. An elegan t possibility of describing anisotropic material behavior based on the micr oplane theory is demonstrated. Its conceptual simplicity originates from th e idea of modeling the material behavior through uniaxial stress-strain law s on several individual material planes. For each plane individual damage l oading functions are introduced allowing for different failure modes. In or der to account for long ranging microstructural mechanisms, second-order gr adients of the strains are incorporated in each of these damage loading fun ctions. The overall response can be determined by an integration of the res ulting microplane laws over the solid angle. The features of gradient enhan ced continuum damage are demonstrated by means of several selected examples . (C) 1999 Elsevier Science B.V. All rights reserved.