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

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 the 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 nonlinear global crack problem corresponding to such a loading in general cannot admit an antisymmetric solution. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1980
Accession Number
ADA088838

Entities

People

  • Rodney A. Stephenson

Organizations

  • California Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Applied Mechanics
  • Boundary Value Problems
  • Cartesian Coordinates
  • Classification
  • Contrast
  • Crack Tips
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Elastic Materials
  • Equations
  • Materials
  • Mathematical Analysis
  • Mechanics
  • Shear Modulus
  • Stresses
  • Traction

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Structural Health Monitoring of Composite Structures.