Speed-dependent tip fields of a moving crack in a hyperelastic material

This paper gives an asymptotic analysis of plane strain deformation and stress fields near the tip of a steady moving crack in a compressible hyperelastic material. The semi-infinite crack is assumed to be in an infinite homogeneous harmonic material under a constant remote mode-I loading. The crack tip deformation and stress fields are derived up to the third order, which ensures the strict positivity of the Jacobian determinant in the vicinity of the moving crack tip. The derived solutions are applied to a specific hyperelastic material for which some recent experimental data are available in the literature. The comparison with the experimental data showed that the crack-face profile and the energy release rate predicted by the present model are in reasonable agreement with experiments and several recent finite-strain elastic models. In addition, the crack branching angle predicted by the present model also agrees well with some known experimental data. All of these results suggest that the harmonic material model has the potential to capture the main features of finite deformation phenomena in the dynamic fracture of hyperelastic materials.