Some Stability Conditions for a Compressible Elastic Material.

Abstract

Two sets of restrictions on the strain-energy function for a compressible isotropic elastic material are obtained which are necessary conditions for stability of the material. These arise from the following considerations. (1) A rectangular block is subjected to a finite pure homogeneous deformation and an infinitesimal pure homogeneous deformation with arbitrary principal directions is superposed. The dimensions in two of these principal directions are held constant. Then the incremental modulus associated with the third principal direction must be positive for stability to obtain. (2) In the initial pure homogeneous deformation one pair of faces of the block is forece-free. The superposed infinitesimal pure homogeneous deformation has one of its principal directions normal to tese faces, which remain force-free, and the principal extension ratio corresponding to another is unity. The incremental modulus corresponding to the third principal direction must be positive for stability to obtain.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1981
Accession Number
ADA097351

Entities

People

  • Kenneth N. Sawyers
  • Ronald S. Rivlin

Organizations

  • Lehigh University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Cartesian Coordinates
  • Classification
  • Coordinate Systems
  • Elastic Materials
  • Elastic Properties
  • Equations
  • Materials
  • Mathematics
  • Mechanics
  • Military Research
  • Permutations
  • Plane Waves
  • Plastic Explosives
  • Security
  • Shear Modulus
  • Stability Conditions
  • Stationary

Fields of Study

  • Mathematics

Readers

  • Mechanical Engineering/Mechanics of Materials.
  • Structural Dynamics.