Geometrical Picture of Third-Order Tensors

Abstract : Because of it strong physical meaning, the decomposition of a symmetric second-order tensor into a deviatoric and a spheric part is heavily used in continuum mechanics. When considering higher-order continua, third-order tensors naturally appear in the formulation of the problem. Therefore researchers had proposed numerous extensions of the decomposition to third-order tensors. But, considering the actual literature, the situation seems to be a bit messy: definitions vary according to authors, improper uses of denomination flourish, and, at the end, the understanding of the physics contained in third-order tensors remains fuzzy. The aim of this paper is to clarify the situation. Using few tools from group representation theory, we will provide an unambiguous and explicit answer to that problem.
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00771244
Contributor : Nicolas Auffray <>
Submitted on : Friday, May 10, 2013 - 2:42:09 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:13 PM
Long-term archiving on : Tuesday, April 4, 2017 - 6:11:55 AM

File

Auf13.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Nicolas Auffray. Geometrical Picture of Third-Order Tensors. H. Altenbach et al. (eds.). Generalized Continua as Models for Materials, Advanced Structured Materials, Springer-Verlag Berlin Heidelberg, pp.17-40, 2013, ⟨10.1007/978-3-642-36394-8_2⟩. ⟨hal-00771244v2⟩

Share

Metrics

Record views

430

Files downloads

293