Modeling the Role of Fiber–Matrix Coupling on the Failure of Biological Tissues

Accurate failure prediction methods are crucial in evaluating the biological tissues prone to failure. These methods have been extensively studied in isotropic modes but remain underexplored in fiber-reinforced biological tissues with varying anisotropies and fiber–matrix coupling effects. This study aims to model the critical role of fiber orientations and invariant coupling in accurately predicting the uniaxial and biaxial failure stresses of biological tissues. The strain energy density is modeled as a function of the invariants [Formula: see text] (matrix) and [Formula: see text] (fiber), incorporating nonlinear coupling exponents ([Formula: see text]). The impact of invariant coupling and fiber orientations on failure behavior is illustrated for anisotropic tissues by comparing anisotropic modes, with and without fiber–matrix coupling effects, to isotropic modes. Variations in failure envelopes are also analyzed for different fiber orientations and degrees of nonlinearity in the coupling terms across uniaxial and non-equibiaxial stretches. Fiber–matrix coupling alters failure envelopes from [Formula: see text] to [Formula: see text], emphasizing its role in tissue modeling. The impact of nonlinear coupling on the ratio of octahedral shear to octahedral normal stresses further underscores its significance in tissue engineering.