A unifying finite strain modeling framework for anisotropic mixed-mode fracture in soft materials

Elastomers and composites made thereof have wide applications, e.g., in automobile, aerospace, and civil engineering. Predicting fracture in such materials is crucial for efficient design and optimum utilization. These materials are oftentimes hyperelastic and anisotropic in nature and in general subjected to mixed mode loading rather than merely pure modes. Soft biological tissues can also be considered anisotropic hyperelastic materials. Computational modeling helps in studying the role of different sources influencing mixed-mode fracture. A unifying thermodynamically consistent anisotropic phase field formulation for modeling the mixed-mode fracture of hyperelastic soft materials like elastomers, elastomeric fiber-reinforced composites, and soft biological tissues at finite strains is proposed and formulated. To model the mechanical response of anisotropic hyperelastic materials subjected to mixed-mode loading, a coupled Neo-Hookean model with orthotropic anisotropy is adopted considering volumetric-deviatoric and a tension-compression decomposition. For modeling the complex crack initiation and propagation, a phase field method based on a power law criterion is adopted by considering a single order parameter as the damage variable. This model is suitable for capturing the overall response of soft fiber-reinforced elastomeric composites as well as soft biological tissues. The proposed model is validated by conducting fracture tests on (a) silicone elastomers, (b) unidirectional fiber-reinforced elastomeric composites, (c) natural rubber reinforced with black carbon, and (d) brain tissue reinforced with axons. The results obtained are compared with experimental and numerical investigations from literature.