Basis-free expressions for derivatives of a subclass of nonsymmetric isotropic tensor functions |
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Authors: | Wang Zhi-qiao Dui Guan-suo |
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Affiliation: | Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, P. R. China |
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Abstract: | The present paper generalizes the method for solving the derivatives of sym- metric isotropic tensor-valued functions proposed by Dui and Chen(2004)to a subclass of nonsymmetric tensor functions satisfying the commutative condition.This subclass of tensor functions is more general than those investigated by the existing methods.In the case of three distinct eigenvalues,the commutativity makes it possible to introduce two scalar functions,which will be used to construct the general nonsymmetric tensor func- tions and their derivatives.In the cases of repeated eigenvalues,the results are acquired by taking limits. |
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Keywords: | nonsymmetric tensor derivative of tensor function scalar function fourth-order tensor |
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