The Equations of Elasticity are Special,

Abstract

In dynamics, the goal is to relate the Second Law of thermodynamics with 'stability'. The work of Ericksen reveals that the Second Law induces stability of an equilibrium state of a thermoelastic material in the range of convexity of internal energy (e.g. at points where energy attains a minimum.) Similarly, it has been shown that smooth adiabatic processes in thermoelasticity, residing in the range of convexity of internal energy, depend continuously upon the initial state, even within the class of processes that develop shock waves. Actually, in certain circumstances, the same result can be established under a mere Strong Ellipticity assumption.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1979
Accession Number
ADA081668

Entities

People

  • C. M. Dafermos

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Adiabatic Processes
  • Applied Mathematics
  • Calculus Of Variations
  • Continuum Mechanics
  • Eigenvalues
  • Elastic Properties
  • Energy
  • Equations
  • Inequalities
  • Materials
  • Mechanics
  • Phase Transformations
  • Rhode Island
  • Shock Waves
  • Thermodynamic Processes
  • Thermodynamics
  • Thermoelasticity

Readers

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