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A note on cross
product between two symmetric second-order tensors
László Szabó |
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Vol. 12 (2017), No. 2, 147–158
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Abstract |
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The present work is concerned with defining the cross product for symmetric, second-order tensors. The operation presented in this paper generalizes the classical vectorial cross product from three-dimensional Euclidean space to symmetric tensor fields on a seven-dimensional vector space. The result of the cross product operation expresses a nonsymmetric tensor as a sum of a symmetric and a skew-symmetric tensor with one parameter, which satisfies the usual properties of the vector cross product except the triple cross product rule. The cross product formulation can be applied to pairs of symmetric or nonsymmetric tensors where the skew-symmetric parts have the same eigenvectors. |
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Keywords
vector cross product, second-order tensors, tensorial cross
product, seven-dimensional vector space
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Milestones
Received: 15 January 2016
Revised: 11 October 2016
Accepted: 15 November 2016
Published: 14 December 2016
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Authors |
| László Szabó | |
| Department of Applied
Mechanics Budapest University of Technology and Economics Müegyetem rkp. 5 Budapest 1111 Hungary |
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