Discussion of thermomechanics on the basis of frame invariance of physical law

Research output: Contribution to journalArticle

Abstract

In continuum mechanics it is not clear what 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 frame transformation laws of constitutive quantities and source quantities are simultaneously derived for a changing frame under the assumption that the forms of the first and second laws of thermodynamics are invariant for changes of frame. Next, considering whether the reverse proposition is true or false, an explanation of the relationship between the PMFI and the invariance of the laws of thermodynamics for changes of frame is given. Then the bases of the PMFI are determined, clarifying the relationship between the PMFI and the frame invariance of the Clausius-Duhem inequality. Moreover, it is indicated that this method, which enables derivation of conservation laws using changes of frame, is equivalent to both the principle of virtual power and the method of Green and Rivlin.

Original languageEnglish
Pages (from-to)7-13
Number of pages7
JournalJSME International Journal, Series A: Mechanics and Material Engineering
Volume37
Issue number1
Publication statusPublished - 1994 Jan

Fingerprint

Invariance
Conservation
Thermodynamics
Continuum mechanics

ASJC Scopus subject areas

  • Engineering(all)

Cite this

@article{f1e0b0eb55ec44e6ab9abc0e744dedbb,
title = "Discussion of thermomechanics on the basis of frame invariance of physical law",
abstract = "In continuum mechanics it is not clear what 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 frame transformation laws of constitutive quantities and source quantities are simultaneously derived for a changing frame under the assumption that the forms of the first and second laws of thermodynamics are invariant for changes of frame. Next, considering whether the reverse proposition is true or false, an explanation of the relationship between the PMFI and the invariance of the laws of thermodynamics for changes of frame is given. Then the bases of the PMFI are determined, clarifying the relationship between the PMFI and the frame invariance of the Clausius-Duhem inequality. Moreover, it is indicated that this method, which enables derivation of conservation laws using changes of frame, is equivalent to both the principle of virtual power and the method of Green and Rivlin.",
author = "Kazuyuki Shizawa",
year = "1994",
month = "1",
language = "English",
volume = "37",
pages = "7--13",
journal = "JSME International Journal, Series 1: Solid Mechanics, Strength of Materials",
issn = "1340-8046",
publisher = "Japan Society of Mechanical Engineers",
number = "1",

}

TY - JOUR

T1 - Discussion of thermomechanics on the basis of frame invariance of physical law

AU - Shizawa, Kazuyuki

PY - 1994/1

Y1 - 1994/1

N2 - In continuum mechanics it is not clear what 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 frame transformation laws of constitutive quantities and source quantities are simultaneously derived for a changing frame under the assumption that the forms of the first and second laws of thermodynamics are invariant for changes of frame. Next, considering whether the reverse proposition is true or false, an explanation of the relationship between the PMFI and the invariance of the laws of thermodynamics for changes of frame is given. Then the bases of the PMFI are determined, clarifying the relationship between the PMFI and the frame invariance of the Clausius-Duhem inequality. Moreover, it is indicated that this method, which enables derivation of conservation laws using changes of frame, is equivalent to both the principle of virtual power and the method of Green and Rivlin.

AB - In continuum mechanics it is not clear what 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 frame transformation laws of constitutive quantities and source quantities are simultaneously derived for a changing frame under the assumption that the forms of the first and second laws of thermodynamics are invariant for changes of frame. Next, considering whether the reverse proposition is true or false, an explanation of the relationship between the PMFI and the invariance of the laws of thermodynamics for changes of frame is given. Then the bases of the PMFI are determined, clarifying the relationship between the PMFI and the frame invariance of the Clausius-Duhem inequality. Moreover, it is indicated that this method, which enables derivation of conservation laws using changes of frame, is equivalent to both the principle of virtual power and the method of Green and Rivlin.

UR - http://www.scopus.com/inward/record.url?scp=0028195773&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028195773&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0028195773

VL - 37

SP - 7

EP - 13

JO - JSME International Journal, Series 1: Solid Mechanics, Strength of Materials

JF - JSME International Journal, Series 1: Solid Mechanics, Strength of Materials

SN - 1340-8046

IS - 1

ER -