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Communication Dans Un Congrès Année : 1983

Non-local modeling: Macroscopic behavior of a randomly voided material and influence of inclusion morphology on the elastic properties gradient

Sami Ben
  • Fonction : Auteur
Elhaj Salah
  • Fonction : Auteur
Azdine Nait- Ali
Mikaël Gueguen

Résumé

The asymptotic expansion analysis was developed in the framework of homogenization technique, which is applicable for three-dimensional composite made up of random inclusions embedded in a matrix. The so-called asymptotic expansion homogenization (AEH) method was developed by Francfort [1] for the case of linear thermoelasticity in periodic structure. The AEH method has been employed to calculate the homogenized thermomechanical properties of composite materials (elastic moduli and coefficient of thermal expansion) [2, 3]. This technique of homogenization enables us to replace heterogeneous materials by a homogeneous equivalent medium including (higher/second) order gradients of displacement [4]. More precisely, the present work is devoted to linear stochastic homogenization and Γ-convergence [5] problems for variational functional. The formulation of AEH method is based on the small deformation theory, and linear elastic assumption is implemented to all unit-cell constituents. Then by combining variational convergence with ergodic theory, we study the macroscopic behavior of random heterogeneous materials. The inclusion are randomly distributed into a matrix, their size is of order η. The variational limit functional energy obtained when η tends to 0 is deterministic and non-local [6,7,8,9].
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Dates et versions

hal-01756046 , version 1 (10-04-2018)

Identifiants

  • HAL Id : hal-01756046 , version 1

Citer

Sami Ben, Elhaj Salah, Azdine Nait- Ali, Carole Nadot, Mikaël Gueguen. Non-local modeling: Macroscopic behavior of a randomly voided material and influence of inclusion morphology on the elastic properties gradient. EMMC, Mar 2018, Nantes, France. pp.696 - 708. ⟨hal-01756046⟩
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