On the Dissipation Associated with Equilibrium Shocks in Finite Elasticity.

Abstract

Equilibrium fields with discontinuous displacement gradients can occur in finite elasticity for certain materials. The presence of such 'equilibrium shocks' affects the energy balance in the elastostatic field, and the present paper is concerned with a notion of dissipation associated with this energy balance. A dissipation inequality is proposed for three-dimensional equilibrium shocks for both compressible and incompressible materials. The consequences of this inequality are studied for weak shocks in plane strain for compressible materials and for shocks of arbitrary strength in anti-plane strain for a class of incompressible materials. A thermodynamic argument for the dissipation inequality is also given. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1977
Accession Number
ADA050031

Entities

People

  • James K. Knowles

Organizations

  • California Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Bodies
  • Boundaries
  • Boundary Value Problems
  • Coordinate Systems
  • Differential Equations
  • Elastic Materials
  • Elastic Properties
  • Energy
  • Engineering
  • Equations
  • Flow
  • Materials
  • Mechanics
  • Partial Differential Equations
  • Shear Modulus
  • Shear Stresses
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Combustion Dynamics and Shock Wave Physics.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.