Crack Propagation in Homogeneous and Bimaterial Sheets Under General In-Plane Loading: Nonlinear Analysis

The problem of non-coplanar crack propagation in homogeneous and bimaterial sheets is investigated within the framework of the nonlinear theory of plane stress and for the Generalized Neo-Hookean class of hyperelastic solids. The analysis is performed numerically using a boundary layer approach and the maximum energy release rate criterion. The influence of the large deformation effect on the limiting process associated with the concept of “infinitesimal virtual crack extension” is examined, together with the possible relation between the size of the nonlinear zone and the additional length parameter appearing in the linearized analysis of the interfacial crack propagation problem. As the virtual crack extension is gradually shortened to a size comparable to that of the nonlinear zone, a transition is observed between the nonunique value of the kink angle predicted by the linearized theory and a single “nonlinear” value, which is independent of the crack extension length but also independent of the far-field loading conditions. In the limit of homogeneous properties this angle is zero and is corroborated by experiments on natural rubber undergoing large deformations.