Explicit Harmonic Structure of Bidimensional Strain-Gradient Elasticity - Mechanics Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Explicit Harmonic Structure of Bidimensional Strain-Gradient Elasticity

Résumé

In the perspective of homogenization theory, strain-gradient elasticity is a strategy to describe the overall behaviour of materials with coarse mesostructure. In this approach, the effect of the mesostructure is described by the use of three elasticity tensors whose orders vary from 4 to 6. Higher-order constitutive tensors make it possible to describe rich physical phenomena. However, these objects have intricate algebraic structures that prevent us from having a clear picture of their modeling capabilities. The harmonic decomposition is a fundamental tool to investigate the anisotropic properties of constitutive tensor spaces. For higher-order tensors (i.e. tensors of order n ≥3), its establishment is generally a difficult task. In this paper a novel procedure to obtain this decomposition is introduced. This method, that we have called the Clebsch-Gordan Harmonic Algorithm, allows to obtain explicit harmonic decompositions satisfying good properties such as orthogonality and unicity. The elements of the decomposition also have a precise geometrical meaning simplifying their physical interpretation. This new algorithm is here developed in the specific case of 2D space and applied to Mindlin's Strain-Gradient Elasticity. We provide, for the first time, the harmonic decompositions of the fifth-and sixth-order elasticity tensors involved in this constitutive law.
Fichier principal
Vignette du fichier
ADA20_final.pdf (596.72 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02900663 , version 1 (16-07-2020)

Identifiants

  • HAL Id : hal-02900663 , version 1

Citer

Nicolas Auffray, Houssam Abdoul-Anziz, Boris Desmorat. Explicit Harmonic Structure of Bidimensional Strain-Gradient Elasticity. 2020. ⟨hal-02900663⟩
52 Consultations
34 Téléchargements

Partager

Gmail Facebook X LinkedIn More