Constitutive Relation for Modelling Anisotropic Fracture in Heterogeneous Materials at Finite Strain

Materials such as elastomeric composites, and soft biological tissues are heterogeneous and anisotropic in nature due to the presence of reinforcements like, fibers, axons, and they undergo large deformations and exhibit nonlinear elastic behavior. To understand the load carrying capacity and fracture phenomena in such materials, a nonlocal phase field model is developed to capture the anisotropic fracture and indigenous heterogeneity. An additive decomposition of strain energy density function is considered, which accounts for both isotropic and anisotropic contributions. The volumetric-isochoric split as well as tension-compression split of the strain energy density function is considered in the proposed model. A crack driving force is defined based on the distinct energy release rates of different constituents of the system. The proposed model is easy and simple to implement and works very well in modelling fracture in heterogeneous systems.