On the inversion of non symmetric sixth-order isotropic tensors and conditions of positiveness of third-order tensor valued quadratic functions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mechanics Research Communications Année : 2011

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

Résumé

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.
Fichier principal
Vignette du fichier
Monchiet-Bonnet-MRC2011.pdf (103.03 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00687815 , version 1 (18-04-2012)

Identifiants

Citer

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, 2011, 38 (4), pp.326-329. ⟨10.1016/j.mechrescom.2011.03.006⟩. ⟨hal-00687815⟩
97 Consultations
309 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More