The Equilibrium Field Near the Tip of a Crack for Finite Plane Strain of Incompressible Elastic Materials

Author: Stephenson, Rodney Alan

Year: 1981

Degree: Dissertation (Ph.D.)

Advisor: Sternberg, Eli

Committee Member: Unknown, Unknown

Option: Applied Mechanics

DOI: 10.7907/y00g-0984

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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