Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions

WANG Zhi-qiao; DUI Guan-suo

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WANG Zhi-qiao, DUI Guan-suo. Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1115-1122.

Citation:

WANG Zhi-qiao, DUI Guan-suo. Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1115-1122.

Citation:

WANG Zhi-qiao, DUI Guan-suo. Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1115-1122.

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Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions

Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, P. R. China

Received Date: 2006-11-03
Rev Recd Date: 2007-03-30
Publish Date: 2007-09-15

Abstract

Abstract

The method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen was generalized to a sub-class 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.
- nonsymmetric tensor,
- derivative of tensor function,
- scalar function,
- fourth-order tensor

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References(18)

References

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