### Abstract

Thermodynamic quantities of state are defined under the nonequilibrium processes by the thermopolar theory. Constitutive equations for thermopolar materials are constructed on the basis of the results of the previous reports. As preliminary data, the arguments of the quasi-conservative part of the constitutive equations are restricted by the Clausius-Duhem inequality derived in the previous report. Moreover, the thermodynamic potentials are discussed; these are not only Helmholz's free energy, but also newly defined thermodynamic potential characterizing thermopolar materials. Then dissipative parts of the constitutive equations are restricted to satisfy the principle of maximal dissipation rate. Furthermore, the constitutive equations for thermopolar materials are constructed thermodynamically on the basis of the above discussion. Consequently, considering the physical interpretations of the linear constitutive equations, it is indicated that both the quasi-conservative internal force and the dissipative internal forces depend on the microscopic gradient of temperature.

Original language | English |
---|---|

Pages (from-to) | 607-613 |

Number of pages | 7 |

Journal | Transactions of the Japan Society of Mechanical Engineers Series A |

Volume | 58 |

Issue number | 548 |

DOIs | |

Publication status | Published - 1992 |

Externally published | Yes |

### Fingerprint

### Keywords

- Constitutive Equation
- Continuum Mechanics
- Material Design
- Microscopic Gradient of Temperature
- Nonequilibrium
- Thermal Stress
- Thermodynamics
- Thermopolar Material

### ASJC Scopus subject areas

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

### Cite this

*Transactions of the Japan Society of Mechanical Engineers Series A*,

*58*(548), 607-613. https://doi.org/10.1299/kikaia.58.607

**Constitutive Equations for Thermopolar Materials with Microscopic Gradient of Temperature.** / Kobayashi, Seiichi; Shizawa, Kazuyuki; Takahashi, Kunihiro.

Research output: Contribution to journal › Article

*Transactions of the Japan Society of Mechanical Engineers Series A*, vol. 58, no. 548, pp. 607-613. https://doi.org/10.1299/kikaia.58.607

}

TY - JOUR

T1 - Constitutive Equations for Thermopolar Materials with Microscopic Gradient of Temperature

AU - Kobayashi, Seiichi

AU - Shizawa, Kazuyuki

AU - Takahashi, Kunihiro

PY - 1992

Y1 - 1992

N2 - Thermodynamic quantities of state are defined under the nonequilibrium processes by the thermopolar theory. Constitutive equations for thermopolar materials are constructed on the basis of the results of the previous reports. As preliminary data, the arguments of the quasi-conservative part of the constitutive equations are restricted by the Clausius-Duhem inequality derived in the previous report. Moreover, the thermodynamic potentials are discussed; these are not only Helmholz's free energy, but also newly defined thermodynamic potential characterizing thermopolar materials. Then dissipative parts of the constitutive equations are restricted to satisfy the principle of maximal dissipation rate. Furthermore, the constitutive equations for thermopolar materials are constructed thermodynamically on the basis of the above discussion. Consequently, considering the physical interpretations of the linear constitutive equations, it is indicated that both the quasi-conservative internal force and the dissipative internal forces depend on the microscopic gradient of temperature.

AB - Thermodynamic quantities of state are defined under the nonequilibrium processes by the thermopolar theory. Constitutive equations for thermopolar materials are constructed on the basis of the results of the previous reports. As preliminary data, the arguments of the quasi-conservative part of the constitutive equations are restricted by the Clausius-Duhem inequality derived in the previous report. Moreover, the thermodynamic potentials are discussed; these are not only Helmholz's free energy, but also newly defined thermodynamic potential characterizing thermopolar materials. Then dissipative parts of the constitutive equations are restricted to satisfy the principle of maximal dissipation rate. Furthermore, the constitutive equations for thermopolar materials are constructed thermodynamically on the basis of the above discussion. Consequently, considering the physical interpretations of the linear constitutive equations, it is indicated that both the quasi-conservative internal force and the dissipative internal forces depend on the microscopic gradient of temperature.

KW - Constitutive Equation

KW - Continuum Mechanics

KW - Material Design

KW - Microscopic Gradient of Temperature

KW - Nonequilibrium

KW - Thermal Stress

KW - Thermodynamics

KW - Thermopolar Material

UR - http://www.scopus.com/inward/record.url?scp=85008286196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85008286196&partnerID=8YFLogxK

U2 - 10.1299/kikaia.58.607

DO - 10.1299/kikaia.58.607

M3 - Article

AN - SCOPUS:85008286196

VL - 58

SP - 607

EP - 613

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

SN - 0387-5008

IS - 548

ER -