Eshelby-Kröner Self-Consistent elastic model: the geometric mean versus the arithmetic mean - A numerical investigation

Sylvain Fréour (1) , Jamal Fajoui (1)

1 E3M - État Mécanique et Microstructure des Matériaux

Scale-transition models, such as Eshelby-Kroner self-consistent framework, which are often used for predicting the effective behavior of heterogeneous materials or estimating the distribution of local states from the knowledge of the corresponding macroscopic quantities, require the extensive use of set averages. The present paper is devoted to the comparison of the numerical results provided in pure elasticity by Eshelby-Kroner model depending on the average type chosen for achieving set average operations: either the traditional arithmetic mean or the geometric average. Various numerical applications of the model to the case of predicting either the effective stiffness or the lattice strains of single-phase polycrystals will be provided. The particular case when an extreme grain-shape occurs will also be investigated.

Mots clés: sets averages; scale transition model; geometric mean; arithmetic mean; Eshelby-Kröner self-consistent model

Domaines: Mécanique des matériaux [physics.class-ph]

Sylvain Fréour, Jamal Fajoui. Eshelby-Kröner Self-Consistent elastic model: the geometric mean versus the arithmetic mean - A numerical investigation. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2012, 92 (4), pp.329-338. ⟨10.1002/zamm.201100135⟩. ⟨hal-01006806⟩