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Use of differential forms in the determination of divergence of cross products of tensors in nonlinear solid mechanics
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Flajs, Rado
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https://onlinelibrary.wiley.com/doi/10.1002/pamm.202300118
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Abstract
We consider the cross product of tensors introduced by R. de Boer (1982) and used by J. Bonet et al. (2016) in describing problems from nonlinear solid mechanics. From the paper by J. Bonet et al., it appears that the cross product of tensors can be used to rearrange the mechanical descriptions and significantly simplify the expressions of selected mechanical quantities encountered in the description of mechanical problems in solid mechanics with large strains. In this paper, we derive some additional properties of the cross product of tensors, which also allow some simplifications of selected mechanical quantities. In particular, we establish a connection between the cross product of operators and differential forms introduced by M. Spivak (1971, 1999). These connections allow further generalization of some expressions. At this point, we take advantage of the important fact that the second differentials of differential forms are zeros. This fact allows further simplification of certain expressions and opens up further new possibilities in the description of mechanical problems in nonlinear solid mechanics.
Language:
English
Keywords:
cross product of tensors
,
nonlinear solid mechanics
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
FGG - Faculty of Civil and Geodetic Engineering
Publication status:
Published
Publication version:
Version of Record
Year:
2023
Number of pages:
8 str.
Numbering:
Vol. 23, iss. 3, art. e202300118
PID:
20.500.12556/RUL-159058
ISSN on article:
1617-7061
DOI:
10.1002/pamm.202300118
Publication date in RUL:
28.06.2024
Views:
133
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37
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Record is a part of a journal
Title:
Proceedings in applied mathematics and mechanics
Shortened title:
Proc. appl. math. mech.
Publisher:
Wiley, Gesellschaft für angewandte Mathematik und Mechanik
ISSN:
1617-7061
COBISS.SI-ID:
7207958
Licences
License:
CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
Link:
http://creativecommons.org/licenses/by-nc/4.0/
Description:
A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.
Projects
Funder:
ARRS - Slovenian Research Agency
Project number:
P2-0260
Name:
Mehanika konstrukcij
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