A NOTE ON CROSS PRODUCT BETWEEN TWO SYMMETRIC SECOND-ORDER TENSORS

摘要

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.