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 language | English |
|---|---|
| Pages (from-to) | 880-886 |
| Number of pages | 7 |
| Journal | Transactions of the Japan Society of Mechanical Engineers Series A |
| Volume | 58 |
| Issue number | 550 |
| DOIs | |
| Publication status | Published - 1992 |
| Externally published | Yes |
Fingerprint
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
Thermodynamical Discussions for Standpoint of Principle of Material Frame Indifference. / Shizawa, Kazuyuki.
In: Transactions of the Japan Society of Mechanical Engineers Series A, Vol. 58, No. 550, 1992, p. 880-886.Research output: Contribution to journal › Article
}
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 -