Variational-Lagrangian Thermodynamics of Non-Linear Thermorheology.

Abstract

A principle of virtual dissipation generalizing d'Alembert's principle to non-linear irreversible thermodynamics provides a unifying foundation which leads to an extremely general variational - Lagrangian analysis of dissipative phenomena. Thus a synthesis is achieved between thermodynamics and classical mechanics. The present paper applies this principle to the non-linear thermomechanics of continua with dissipation and heat conduction. Field equations, constitutive equations and Lagrangian equations with generalized coordinates are derived for non-linear thermoviscoelasticity, non-linear thermoelasticity and heat conduction, plasticity, and compressible heat conducting fluids with Newtonian and non-Newtonian viscosity. The thermodynamics of instability is also analyzed from the same fundamental viewpoint.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1974
Accession Number
ADA012987

Entities

People

  • Maurice A. Biot

Tags

DTIC Thesaurus Topics

  • Constitutive Equations
  • Dissipation
  • Equations
  • Equations Of State
  • Heat Energy
  • Mechanical Properties
  • Mechanics
  • Molecular Mechanics Methods
  • Plastic Properties
  • Thermodynamics
  • Thermomechanics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.