### Abstract

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 viscoelasticity. 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 noninstantaneities 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 language | English |
---|---|

Pages (from-to) | 225-231 |

Number of pages | 7 |

Journal | Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A |

Volume | 59 |

Issue number | 557 |

Publication status | Published - 1993 Jan |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*,

*59*(557), 225-231.

**Thermodynamic discussions for continua considering noninstantaneities.** / Kobayashi, Seiichi; Shizawa, Kazuyuki; Takahashi, Kunihiro.

Research output: Contribution to journal › Article

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*, vol. 59, no. 557, pp. 225-231.

}

TY - JOUR

T1 - Thermodynamic discussions for continua considering noninstantaneities

AU - Kobayashi, Seiichi

AU - Shizawa, Kazuyuki

AU - Takahashi, Kunihiro

PY - 1993/1

Y1 - 1993/1

N2 - 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 viscoelasticity. 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 noninstantaneities 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.

AB - 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 viscoelasticity. 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 noninstantaneities 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.

UR - http://www.scopus.com/inward/record.url?scp=0027201291&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027201291&partnerID=8YFLogxK

M3 - Article

VL - 59

SP - 225

EP - 231

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 - 557

ER -