Basic Equations for Continua Considering Microscopic Curvature of Temperature

Seiichi Kobayashi, Kazuyuki Shizawa, Kunihiro Takahashi

Research output: Contribution to journalArticlepeer-review


In the previous paper, the thermodynamic behavior of materials for nonequilibrium processes was discussed in continuum mechanics. The spatial nonequilibrium of thermodynamic quantities have been treated as their nonlocalities there. Then balance laws for the above materials under nonequilibrium processes have been derived introducing the nonlocalities of thermodynamic quantities. In the present paper, the constitutive equations for the above materials are constructed on the basis of the previous results to satisfy the thermodynamic relations which are expressed by the newly defined thermodynamic potential and by the dissipative function. Moreover, the basic equation system is shown, substituting the above constitutive equations into balance laws. Furthermore, the relationships among the moduli defined in the constitutive equations, are indicated. As a result, it is clarified that the heat conduction depends on not only the temperature gradient but also microscopic gradient and microscopic curvature of temperature under nonequilibrium processes.

Original languageEnglish
Pages (from-to)868-875
Number of pages8
JournalTransactions of the Japan Society of Mechanical Engineers Series A
Issue number559
Publication statusPublished - 1993
Externally publishedYes


  • Constitutive Equation
  • Entropy
  • Material Design
  • Micropolar Materials
  • Nonequilibrium
  • Nonlocality
  • Thermal Stress
  • Thermodynamics
  • Thermopolar Materials

ASJC Scopus subject areas

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


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