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Applied Mathematics and Mechanics

, Volume 28, Issue 9, pp 1249–1257 | Cite as

Basis-free expressions for derivatives of a subclass of nonsymmetric isotropic tensor functions

  • Wang Zhi-qiao  (王志乔)
  • Dui Guan-suo  (兑关锁)Email author
Article
  • 38 Downloads

Abstract

The present paper generalizes the method for solving the derivatives of symmetric 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 functions and their derivatives. In the cases of repeated eigenvalues, the results are acquired by taking limits.

Key words

nonsymmetric tensor derivative of tensor function scalar function fourth-order tensor 

Chinese Library Classification

O331 O183.2 

2000 Mathematics Subject Classification

74A20 74C15 

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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Wang Zhi-qiao  (王志乔)
    • 1
  • Dui Guan-suo  (兑关锁)
    • 1
    Email author
  1. 1.Institute of Engineering MechanicsBeijing Jiaotong UniversityBeijingP. R. China

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