On the inversion of non symmetric sixth-order isotropic tensors and conditions of positiveness of third-order tensor valued quadratic functions

Abstract : In the present paper we propose new results concerning linear tensorial algebra for third-order and non symmetric isotropic sixth-order tensors in the most general case (i.e. having not the major and minor symmetries). Such tensors are used, for instance, in the theory of microstructured elastic media. A formalism based on an irreducible basis for isotropic sixth-order tensors is introduced, which is useful for performing the classical tensorial operations. Specially, a condensed expression for the product between two isotropic sixth-order tensors is provided, which allows the obtaining of a condition on these tensors for being invertible and a closed form expression of the inverse of such a tensor. Finally, the condition of positiveness of third-order tensor-valued quadratic functions is derived. For instance, such conditions are required for computing the elastic energy of microstructured media.
Complete list of metadatas

Cited literature [8 references]  Display  Hide  Download

https://hal-upec-upem.archives-ouvertes.fr/hal-00687815
Contributor : Vincent Monchiet <>
Submitted on : Wednesday, April 18, 2012 - 10:36:22 AM
Last modification on : Wednesday, September 4, 2019 - 1:52:13 PM
Long-term archiving on : Thursday, July 19, 2012 - 2:21:08 AM

File

Monchiet-Bonnet-MRC2011.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Vincent Monchiet, Guy Bonnet. On the inversion of non symmetric sixth-order isotropic tensors and conditions of positiveness of third-order tensor valued quadratic functions. Mechanics Research Communications, Elsevier, 2011, 38 (4), pp.326-329. ⟨10.1016/j.mechrescom.2011.03.006⟩. ⟨hal-00687815⟩

Share

Metrics

Record views

251

Files downloads

286