Ordinary and Strong Ellipticity in the Equilibrium Theory of Incompressible Hyperelastic Solids.

Abstract

In this paper explicit necessary and sufficient conditions are established for the ordinary and strong ellipticity of the three-dimensional field equations in the nonlinear equilibrium theory of incompressible, homogeneous and isotropic, hyperelastic solids. The resulting system of inequalities involves the local principal stretches directly and in addition restricts the first and second partial derivatives of the strain-energy density with respect to the deformation invariants or the principal stretches. The conditions of ordinary and strong ellipticity are found to coalesce for materials that obey the Baker-Ericksen inequalities and possess a positive shear modulus at infinitesimal deformations. Various implications of these ellipticity conditions for special classes of materials and deformations are explored. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1982
Accession Number
ADA119047

Entities

People

  • Eli Sternberg
  • Layne Zee

Organizations

  • California Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Biaxial Stresses
  • Boundary Value Problems
  • Computational Science
  • Differential Equations
  • Elastic Materials
  • Equations
  • Equations Of Motion
  • Hyperelastic Materials
  • Inequalities
  • Materials
  • Mechanical Properties
  • Mechanics
  • Military Research
  • Molecular Dynamics
  • Partial Differential Equations
  • Shear Modulus
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Materials Science (Mechanical Engineering).
  • Mathematical Modeling and Probability Theory.
  • Structural Dynamics.