Crack tip fields in a neo-Hookean sheet reinforced by nonlinear fibers

In this paper, we derive the asymptotic crack tip fields in a neo-Hookean material reinforced by nonlinear fibers. The fiber are characterized by a power law model which exhibits significant stiffening behavior at large stretch. A specific case of the model yields the so-called standard reinforcing model (Triantafyllidis and Abeyaratne, 1983). A series of transformations is used to set the stage for the asymptotic solution. We begin with a coordinate scaling (Liu and Moran, 2020b) to account for fiber orientation aspects. This is followed by a hodograph transformation to the strain plane to deal with nonlinearities. Finally, an additional nonlinear algebraic transformation is employed to render the equations suitable for a separable solution. The asymptotic solutions are compared with and agree well with finite element solutions for different fiber modulus ratios, fiber orientation angles, and loading modes. We find that, due to the stiffening effects of the fibers, the deformation fields can be divided into three regions, where the deformation in the two regions near to the crack faces is significantly larger than in the middle region. Stress peaks are observed at the interfaces between regions. The solutions in the paper may provide insight into damage modes and crack initiation at a crack tip in fiber-reinforced soft composites.