Thermodynamic Discussions for Continua Considering Noninstantaneities

Seiichi Kobayashi, Kazuyuki Shizawa, Kunihiro Takahashi

Research output: Contribution to journalArticlepeer-review


In conventional theory, it is assumed that continuum state can be determined instantaneously. This assumption restricts the arguments for quantities of state and constitutive equations. In a previous paper, noninstantaneities were introduced in the laws of thermodynamics, to express the constitutive equation of stress including the effect of viscoelastisity. In this paper, we discuss that nonequilibrium processes can be expressed by means of this concept of noninstantaneities in continuum mechanics. The 1st and 2nd laws of thermodynamics are expressed considering the effect of the nonistantaneities of thermodynamic quantities. Then a balance law for the newly defined entropy flux in this paper, is formulated to make the balance equation system complete. Furthermore, the Clausius-Duhem inequality that characterizes materials with the noninstantaneous state is derived. On the basis of the Clausius-Duhem inequality, it is suggested that the constitutive equation of stress restricted thermodynamically, depends on the time rate of the temperature for the nonequilibrium processes.

Original languageEnglish
Pages (from-to)225-231
Number of pages7
JournalTransactions of the Japan Society of Mechanical Engineers Series A
Issue number557
Publication statusPublished - 1993 Jan 1
Externally publishedYes


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

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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