A note on cross product between two symmetric second-order tensors

Szabó, László

doi:10.2140/jomms.2017.12.147

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A note on cross product between two symmetric second-order tensors

László Szabó

Vol. 12 (2017), No. 2, 147–158

DOI: 10.2140/jomms.2017.12.147

Abstract

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.

Keywords

vector cross product, second-order tensors, tensorial cross product, seven-dimensional vector space

Milestones

Received: 15 January 2016

Revised: 11 October 2016

Accepted: 15 November 2016

Published: 14 December 2016

Authors

László Szabó
Department of Applied Mechanics Budapest University of Technology and Economics Müegyetem rkp. 5 Budapest 1111 Hungary

Vol. 12, No. 2, 2017

László Szabó

Abstract

Keywords

Milestones

Authors