Crack tip fields in a fiber-reinforced hyperelastic sheet: Competing roles of fiber and matrix stiffening

Fiber-reinforced materials are widely observed in biological tissue such as human arteries and tendons. Characterizing the influence of fibers on crack-tip fields in such nonlinear materials undergoing large deformation is an important precursor to understanding damage evolution and fracture or tearing. In this paper, we present asymptotic crack tip fields in a fiber-reinforced hyperelastic sheet and explore the competing roles of fiber and matrix stiffening. A generalized neo-Hookean model and a power-law model are employed to characterize the behavior of the matrix and fibers, respectively. We show that the asymptotic crack-tip fields are mainly determined by the phase with largest degree of stiffening. For example, when the stiffening effect of fibers is much larger than that of the matrix, the crack tip fields are determined by the constitutive behavior of fibers, and the wire model and the fabric model reasonably characterize the deformation and stress near the crack tip. On the contrary, if the matrix stiffening is larger than that of the fibers, we show that the crack tip fields approach those of a pure matrix material. The asymptotic results are complemented by finite element simulations which show good agreement. These findings may shed light on material damage at a crack tip in fiber reinforced materials.