Exact expansions of arbitrary tensor functions \(\mathbf F(\mathbf A)\) and their derivatives.
type: Item
instance of: scholarly article
title: Exact expansions of arbitrary tensor functions \(\mathbf F(\mathbf A)\) and their derivatives.
zbMATH Open document ID: 1053.53009
author: Jia Lu
published in: International Journal of Solids and Structures
publication date: 2004-05-27T00:00:00Z
review text: Let \(\mathbf A\) be a second order tensor in an \(n\)-dimensional Euclidean space, and \(\mathbf F(\mathbf A)\) a tensor function defined by the power series. A method is presented for determining the exact expansions of \(\mathbf F(\mathbf A)\). It is shown that \(\mathbf F(\mathbf A)\) can be obtained by differentiating a scalar function of the eigenvalues of \(\mathbf A\). In two- and three-dimensional cases, closed-form, singularity-free expressions of arbitrary tensor functions and their first derivatives are deduced.
Mathematics Subject Classification ID: 53A45
Mathematics Subject Classification ID: 15A72
zbMATH DE Number: 2066458
zbMATH Keywords: tensor functions
zbMATH Keywords: matrix polynomials
zbMATH Keywords: exponential map
zbMATH Keywords: derivative
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
full work available at URL: j.ijsolstr.2003.10.004
OpenAlex ID: W2052171263
DOI: 10.1016/J.IJSOLSTR.2003.10.004
Recommended article: Comments on ``Exact expansions of arbitrary tensor functions \(\mathbf{F(A)}\) and their derivatives''
Recommended article: Discussion on ``Exact expansions of arbitrary tensor functions \(\mathbf{F(A)}\) and their derivatives''
Recommended article: Author's closure: discussion on ``Exact expansions of arbitrary tensor functions \(\mathbf{F(A)}\) and their derivatives''
Recommended article: The exact derivative of the exponential of an unsymmetric tensor
Recommended article: The Derivation of Tensors from Tensor Functions
Recommended article: Computation of the exponential and other isotropic tensor functions and their derivatives.
Recommended article: On the derivative of some tensor-valued functions
Recommended article: Higher derivatives and the inverse derivative of a tensor-valued function of a tensor
description: scientific article; zbMATH DE number 2066458