Evaluation of asymptotic stress field around a crack tip for Neo-Hookean hyperelastic materials

The near-tip asymptotic mechanical field in plane Neo-Hookean hyperelastic media is characterized by the appearance of two singular terms and, as a consequence, needs to be described by four stress parameters. Direct computation of the asymptotic stress field therefore appears to be difficult. In this paper, we propose two pairs of contour integrals. The integrals are shown to be path-independent in a modified sense and so they can be evaluated by using finite element approximations with sufficient accuracy. Also, the relationship between these integrals and the stress parameters is analytically derived. Once the integrals are accurately computed, the stress parameters and, consequently, the asymptotic stress field can then be properly determined. The formulation is considered to be suited for problems under large deformation and subjected to general far-field mixed-mode loads. No particular singular elements are used in the calculations.