Use of differential forms in the determination of divergence of cross products of tensors in nonlinear solid mechanics

Flajs, Rado (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: cross product of tensors, nonlinear solid mechanics
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.08 - Objavljeni znanstveni prispevek na konferenci
• Organizacija: FGG - Fakulteta za gradbeništvo in geodezijo
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: 8 str.
• Številčenje: Vol. 23, iss. 3, art. e202300118
• PID: 20.500.12556/RUL-159058
• ISSN pri članku: 1617-7061
• DOI: 10.1002/pamm.202300118
• COBISS.SI-ID: 203411715
• Datum objave v RUL: 28.06.2024

FLAJS, Rado, 2023, Use of differential forms in the determination of divergence of cross products of tensors in nonlinear solid mechanics. V : Proceedings in applied mathematics and mechanics [na spletu]. Objavljeni znanstveni prispevek na konferenci. 2023. [Dostopano 5 maj 2025]. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=159058

Gradivo je del revije

• Naslov: Proceedings in applied mathematics and mechanics
• Skrajšan naslov: Proc. appl. math. mech.
• Založnik: Wiley, Gesellschaft für angewandte Mathematik und Mechanik
• ISSN: 1617-7061
• COBISS.SI-ID: 7207958

Licence

• Licenca: CC BY-NC 4.0, Creative Commons Priznanje avtorstva-Nekomercialno 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc/4.0/deed.sl
• Opis: Licenca Creative Commons, ki prepoveduje komercialno uporabo, vendar uporabniki ne rabijo upravljati materialnih avtorskih pravic na izpeljanih delih z enako licenco.

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P2-0260
• Naslov: Mehanika konstrukcij