Basic Equations for Continua Considering Noninstantaneities

Seiichi Kobayashi, Kazuyuki Shizawa, Kunihiro Takahashi

Research output: Contribution to journalArticlepeer-review


In the previous paper, noninstantaneities of thermodynamic quantities were introduced in the laws of thermodynamics, to express nonequilibrium processes for continua. Then it was discussed that the time rate of temperature must be newly added to the set of state variables for materials under nonequilibrium processes. In the present paper, the thermodynamic relationships for the above materials are derived and expressed by a newly defined thermodynamic potential and by a dissipation function. Moreover, the constitutive equations are obtained on the basis of the previous results to satisfy the above relationships. The system of basic equations for the continua considering noninstantaneities of thermodynamic quantities is shown, by substituting the constitutive equations into balance laws derived in the previous paper. As a result, it is clarified that the effect of new thermal stress is introduced in the equation of motion and that the velocity of propagation of temperature is finite in the equation of heat conduction according to this theory.

Original languageEnglish
Pages (from-to)2885-2892
Number of pages8
JournalTransactions of the Japan Society of Mechanical Engineers Series A
Issue number568
Publication statusPublished - 1993
Externally publishedYes


  • Constitutive Equation
  • Continuum Mechanics
  • Entropy
  • Memory
  • Nonequilibrium
  • Noninstantaneity
  • Thermal Stress
  • Thermodynamics
  • Thermomechanics

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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