Tensor Algebra and Tensor Analysis for Engineers by Mikhail Itskov

Author:Mikhail Itskov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5. Fourth-Order Tensors

Mikhail Itskov1

(1)Department of Continuum Mechanics, RWTH Aachen University, Kackertstr. 9, 52072 Aachen, Germany

Mikhail Itskov

Email: [email protected]

5.1 Fourth-Order Tensors as a Linear Mapping

Fourth-order tensors play an important role in continuum mechanics where they appear as elasticity and compliance tensors. In this section we define fourth-order tensors and learn some basic operations with them. To this end, we consider a set of all linear mappings of one second-order tensor into another one within . Such mappings are denoted by a colon as

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