On the Ellipticity of the Equations of Nonlinear Elastostatics for a Special Material.

Abstract

This paper deals with the ellipticity of the equations of finite elastostatics for a compressible material that corresponds to a special choice of the strain-energy density and has received repeated attention in the literature. The possible failure of ellipticity of the appropriate system of displacement equations of equilibrium at solutions involving large deformations was suggested by certain difficulties encountered in an attempt to determine the deformations and stresses arising in such a material near the tip of a crack. It is shown here that ellipticity prevails only if the principal stretches are suitably restricted and breaks down, in particular, at a local state of uni-axial tension or compression of sufficiently severe intensity.

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1975
Accession Number
ADA011076

Entities

People

  • Eli Sternberg
  • James K. Knowles

Organizations

  • California Institute of Technology

Tags

DTIC Thesaurus Topics

  • Compression
  • Displacement
  • Equations
  • Intensity
  • Literature
  • Materials
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Structural Dynamics.
  • Theoretical Analysis.