Three-dimensional singular elastostatic fields in a cracked Neo-Hookean hyperelastic solid

The boundary-value problem of Neo-Hookean incompressible hyperelastic cracked solid under a superposition of a plane deformation to an anti-plane one is formulated. An asymptotic analysis is then employed to compute the elastostatic fields near the crack front and their principal properties are illustrated. In a particular basis, the crack is bound to open independently of the magnitude and the mode of the boundary conditions at infinity. The stress field components have different singularities and each one can posses more than one singular term. Some disagreements with the linear theory are evidenced.