Large deformation near a crack tip in a fiber-reinforced neo-Hookean sheet

The asymptotic fields at the tip of a crack in a fiber-reinforced neo-Hookean sheet are derived. The investigation is carried out for the case of a strain energy function for a fiber-reinforced hyperelastic material motivated by composite mechanics (Guo et al., 2006, 2007ab), where the fibers are also neo-Hookean. The resulting asymptotic deformation and stress fields depend qualitatively and quantitatively on the degree of fiber reinforcement. For suitable choice of parameters, the strain energy potential for the material reduces to that of a pure neo-Hookean material and the corresponding asymptotic fields to those obtained by Knowles and Sternberg (1983). The result obtained may prove useful in providing a framework for future exploration in modeling and assessing the mechanical behavior near a slit or tear in soft biological tissue reinforced by collagen fibers and in other applications of fiber-reinforced soft materials.