The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials

Citation

Stephenson, Rodney Alan (1981) The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/y00g-0984. https://resolver.caltech.edu/CaltechETD:etd-10052006-094802

Abstract

This investigation is concerned with the deformations and stresses in a slab of all-around infinite extent containing a traction-free plane crack, under conditions of plane strain. The analysis is carried out within the framework of the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids. For a fairly wide class of such materials and general loading conditions at infinity, asymptotic estimates appropriate to the various field quantities near the crack-tips are deduced. For a subclass of the materials considered, these results -- in contrast to the analogous predictions of the linearized theory -- lead to the conclusion that the crack opens up in a neighborhood of its tips even if the applied loading is antisymmetric about the plane of the crack, (e.g., Mode II loading). It is shown further that the non-linear global crack problem corresponding to such a loading in general cannot admit an antisymmetric solution.

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