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Analysis of Tensor Functions

  • Mikhail Itskov
Chapter
Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

Let us consider a real scalar-valued function \(f\left( \mathbf {A}_1,\mathbf {A}_2,\ldots ,\mathbf {A}_l\right) \) of second-order tensors \(\mathbf {A}_k\in \mathbf {L}\text {in}^n \, \left( k=1,2,\ldots , l\right) \). The function f is said to be isotropic if
$$\begin{aligned}&f\left( \mathbf {Q}\mathbf {A}_1\mathbf {Q}^\text {T},\mathbf {Q}\mathbf {A}_2\mathbf {Q}^\text {T},\ldots , \mathbf {Q}\mathbf {A}_l\mathbf {Q}^\text {T}\right) \nonumber \\&\qquad \qquad \qquad \qquad \qquad =f\left( \mathbf {A}_1,\mathbf {A}_2,\ldots ,\mathbf {A}_l\right) , \quad \forall \mathbf {Q}\in \mathbf {O}\text {rth}^n. \end{aligned}$$

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Continuum MechanicsRWTH Aachen UniversityAachenGermany

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