An asymptotic finite plane deformation analysis of the elastostatic fields at a crack tip in the framework of hyperelastic, isotropic, and nearly incompressible neo-Hookean materials under mode-I loading

In this work, stress and displacement fields were computed around a crack tip in the case of nearly incompressible and isotropic neo-Hookean material. The constitutive equation was linearized, so that the Cauchy stress tensor could be written as a sum of two components: the linear response in term of elastic Hooke’s law and the nonlinear one. Based on this decomposition, an asymptotic analysis has been developed, the fields of linear elastic fracture mechanics (LEFM-theory) are the zero-order terms of the asymptotic expansion. The validity of the proposed theory has been checked in the case of a mode-I crack problem. A numerical model was constructed using a finite element method. It has shown that the computed fields arising from this theory are qualitatively in agreement with those of the finite element simulations.