20.500.12556/RUL-159058 Use of differential forms in the determination of divergence of cross products of tensors in nonlinear solid mechanics 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. cross product of tensors nonlinear solid mechanics true false true Angleški jezik Ni določen Članek v reviji 2024-06-28 15:04:39 2024-06-28 15:04:41 2024-08-19 10:56:23 0000-00-00 00:00:00 2023 0 0 8 str. iss. 3, art. e202300118 Vol. 23 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1617-7061 10.1002/pamm.202300118 203411715 Proc_Appl_Math_and_Mech_-_2023_-_Flajs_-_Use_of_differential_forms_in_the_determination_of_divergence_of_cross_products_of.pdf Proc_Appl_Math_and_Mech_-_2023_-_Flajs_-_Use_of_differential_forms_in_the_determination_of_divergence_of_cross_products_of.pdf 1 25AA1559127EF1593CF4A7355D06060F 69fcb556fb9779f38ac7041cb8b05788dcb61d93ce2d67e86f6adf8f861dfcaa def7a1fa-3551-11ef-8882-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=186843 https://onlinelibrary.wiley.com/doi/10.1002/pamm.202300118 0 c8a92d16-3551-11ef-8882-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=186842 Fakulteta za gradbeništvo in geodezijo 0 0 0