Bi-Dissipative Thick Level Set (TLS) Damage Model for Quasi-Brittle Materials

The Thick Level Set (TLS) approach applied to damage models allows for a nonlocal treatment that prevents from spurious localization problems. In previous works, isotropic damage models with a single scalar parameter were adopted. Under these conditions, a single level set was used to separate the undamaged zone from the damaged zone, and damage growth was expressed as a level set propagation. Schematically, in the damaged zone, the damage variable directly depended on the level set through an explicit function. Beyond a critical length, material was assumed as fully damaged, thus allowing for a natural transition from damage to localized cracking (i.e., strain localization). In this paper, a first step toward the extension of the TLS approach to “bi-dissipative” isotropic damage models is presented. In the adopted formulation, degradation of material properties under prevailing compressive/tensile loading conditions is separately treated. Two distinct damage variables and activation criteria are used. This allows taking into account the degradation of material properties in tension due to compressive damage (for the moment, no unilateral effect is accounted for). In the article, the local damage model and its mathematical properties are discussed first. A strategy for dealing with bi-dissipative damage in the framework of a TLS approach is then presented.