Thermodynamical Discussions for Standpoint of Principle of Material Frame Indifference

Research output: Contribution to journalArticle

Abstract

In continuum mechanics it is not clear what kind of principle is equivalent to the principle of material frame indifference (PMFI). In the present paper, it is first shown that not only mechanical conservation laws but also rules of frame transformation for constitutive quantities and source quantities are simultaneously derived by changing frame on the assumption that the forms of the first and second laws of thermodynamics are invariant for the changes of frame. Next, considering whether the reverse proposition is true or false, an explanation is given for the relation between the PMFI and the invarinance of the laws of thermodynamics for the changes of frame. Then the essential standpoint of PMFI is definitely placed, making the relation between the PMFI and the frame-invariance of Clausius-Duhem inequality clear. Moreover it is indicated that the method which derives the conservation laws using the changes of frame is equivalent to both the principle of virtual power and the method by Green-Rivlin.

Original languageEnglish
Pages (from-to)880-886
Number of pages7
JournalTransactions of the Japan Society of Mechanical Engineers Series A
Volume58
Issue number550
DOIs
Publication statusPublished - 1992
Externally publishedYes

Fingerprint

Conservation
Thermodynamics
Continuum mechanics
Invariance

Keywords

  • Conservation Laws
  • Constitutive Equation
  • Continuum Mechanics
  • Elasticity
  • Energy Principle
  • Frame Indifference
  • Objectivity
  • Thermodynamics

ASJC Scopus subject areas

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

Cite this

@article{7f843f7c5a7c4c719ee4c7e68d6954b0,
title = "Thermodynamical Discussions for Standpoint of Principle of Material Frame Indifference",
abstract = "In continuum mechanics it is not clear what kind of principle is equivalent to the principle of material frame indifference (PMFI). In the present paper, it is first shown that not only mechanical conservation laws but also rules of frame transformation for constitutive quantities and source quantities are simultaneously derived by changing frame on the assumption that the forms of the first and second laws of thermodynamics are invariant for the changes of frame. Next, considering whether the reverse proposition is true or false, an explanation is given for the relation between the PMFI and the invarinance of the laws of thermodynamics for the changes of frame. Then the essential standpoint of PMFI is definitely placed, making the relation between the PMFI and the frame-invariance of Clausius-Duhem inequality clear. Moreover it is indicated that the method which derives the conservation laws using the changes of frame is equivalent to both the principle of virtual power and the method by Green-Rivlin.",
keywords = "Conservation Laws, Constitutive Equation, Continuum Mechanics, Elasticity, Energy Principle, Frame Indifference, Objectivity, Thermodynamics",
author = "Kazuyuki Shizawa",
year = "1992",
doi = "10.1299/kikaia.58.880",
language = "English",
volume = "58",
pages = "880--886",
journal = "Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A",
issn = "0387-5008",
publisher = "Japan Society of Mechanical Engineers",
number = "550",

}

TY - JOUR

T1 - Thermodynamical Discussions for Standpoint of Principle of Material Frame Indifference

AU - Shizawa, Kazuyuki

PY - 1992

Y1 - 1992

N2 - In continuum mechanics it is not clear what kind of principle is equivalent to the principle of material frame indifference (PMFI). In the present paper, it is first shown that not only mechanical conservation laws but also rules of frame transformation for constitutive quantities and source quantities are simultaneously derived by changing frame on the assumption that the forms of the first and second laws of thermodynamics are invariant for the changes of frame. Next, considering whether the reverse proposition is true or false, an explanation is given for the relation between the PMFI and the invarinance of the laws of thermodynamics for the changes of frame. Then the essential standpoint of PMFI is definitely placed, making the relation between the PMFI and the frame-invariance of Clausius-Duhem inequality clear. Moreover it is indicated that the method which derives the conservation laws using the changes of frame is equivalent to both the principle of virtual power and the method by Green-Rivlin.

AB - In continuum mechanics it is not clear what kind of principle is equivalent to the principle of material frame indifference (PMFI). In the present paper, it is first shown that not only mechanical conservation laws but also rules of frame transformation for constitutive quantities and source quantities are simultaneously derived by changing frame on the assumption that the forms of the first and second laws of thermodynamics are invariant for the changes of frame. Next, considering whether the reverse proposition is true or false, an explanation is given for the relation between the PMFI and the invarinance of the laws of thermodynamics for the changes of frame. Then the essential standpoint of PMFI is definitely placed, making the relation between the PMFI and the frame-invariance of Clausius-Duhem inequality clear. Moreover it is indicated that the method which derives the conservation laws using the changes of frame is equivalent to both the principle of virtual power and the method by Green-Rivlin.

KW - Conservation Laws

KW - Constitutive Equation

KW - Continuum Mechanics

KW - Elasticity

KW - Energy Principle

KW - Frame Indifference

KW - Objectivity

KW - Thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=84998345051&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84998345051&partnerID=8YFLogxK

U2 - 10.1299/kikaia.58.880

DO - 10.1299/kikaia.58.880

M3 - Article

AN - SCOPUS:84998345051

VL - 58

SP - 880

EP - 886

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 - 550

ER -