Stress-gradient model for tensile damage in orthotropic materials

Reliable finite element simulation of orthotropic-dependent failure mechanisms is crucial for understanding the mechanical behavior and optimizing engineered composites and fiber-based materials. Such materials behave brittle under tension and strongly depend on the orthotropic material orientation. Existing non-local models can reproduce brittle fracture for isotropic materials but, in most cases, they are based on the equivalent strain concept for damage initiation, which is unsuitable for orthotropic materials. This contribution introduces a stress-based non-local damage model enhanced with an implicit gradient formulation of the failure criteria. A localizing non-local length is assumed to avoid any pathological broadening of the damage band. The methodology introduces direction-dependent damage variables driven by non-local stress-based damage criteria and can thus distinguish different failure modes. The verification and validation are shown on numerical and experimental benchmark examples. The implicit gradient-based non-local damage approach allows mesh-independent results. Furthermore, it does not require a priori known crack paths and makes it possible to simulate complex failure modes. Perspectively, its effective implementation in the commercial software Abaqus and combination with other constitutive laws, e.g. to account for plasticity or moisture, make it an attractive tool for describing the mechanical material behavior of orthotropic materials, such as wood and fiber-composites.