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.

This contribution aims for an enhanced numerical representation for strength prediction of timber. This implies a validated elasto-plastic continuum damage model which considers orthotropy and heterogeneity of the material, and represents the ductile behavior under compression and the brittle material behavior under tension dependent on the three-dimensional orthogonal fiber directions. The behavior under compression is captured by Hill (1948) plasticity and an exponential hardening law enhanced by the loading direction dependency. The same model covers also the brittle damaging behavior by means of continuum damage mechanics (CDM). In this study, a separated damage mode (SDM) criterion with simultaneously evolving damage variables is investigated. After the experimental validation of the model for axially loaded clear wood samples, the developed numerical model is implemented to a sawn timber with fiber deviation, where homogenization of the material and simplification to transverse isotropy is not anymore possible. The 3D orthotropic material behavior is experimentally validated for this application example with bi-axial loading and aims for further numerical investigation of wood with heterogeneities as occurring in sawn (hard)wood for its efficient use in engineered wood products such as glued laminated timber.