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


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.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Sternberg, Eli
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 July 1980
Record Number:CaltechETD:etd-10052006-094802
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3931
Deposited By: Imported from ETD-db
Deposited On:13 Oct 2006
Last Modified:16 Apr 2021 23:20

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PDF (Stephenson_ra_1981.pdf) - Final Version
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