A plane strain analysis of the elastostatic fields near the notch-tip of a Blatz-Ko material

Abstract

An asymptotic plane strain analysis is carried out in order to study the notch problem in a homogeneous isotropic compressible hyperelastic material whose behavior is governed by the Blatz-Ko constitutive law. The work is realized within the framework of the fully nonlinear fracture mechanics at large strain. Close to the notch tip, a stress-free state is assumed in the notch edges, while at infinity (sufficiently far to the notch tip) fracture modes I and II are considered. The results emphasizes many discrepancies with linear theory predictions like the emergence of a logarithmic singularity and show that solution depends on the notch initial opening angle.