Stochastic homogenization of reinforced polymer with very small carbon inclusions

Azdine Nait- Ali (1)

1 ENDO - ENDOmmagement et durabilité [Institut Pprime]

In this study, we wish to determine a homogenized model of a material reinforced by spherical inclusion that is randomly distributed in space. The method used for the transition to the limit is Γ-convergence [1] in the stochastic case. In addition to the stochastic framework, the very small size compared to the characteristic size of the materials makes the homogenization procedure unconventional. In this study, we want to determine a homogenized model of a material reinforced by a spherical inclusion distributed randomly in space. The peculiarity here is that these particles are of very small size, this generating an energy due to the strong contrast of microstructure. The method used for the transition to the limit is Γ-convergence [1] in the stochastic case. The random distribution is taken into account during the transition of scales, so as to preserve the statistical information, and that in spite of the passage to the limit. In addition to the stochastic framework, the very small size compared to the characteristic size of the materials makes the homogenization procedure unconventional.

Mots clés: Asymptotic analysis; Γ-convergence; Ergodic theory

Domaines: Mécanique des fluides [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Acoustique [physics.class-ph]; Automatique / Robotique; Electromagnétisme; Milieux fluides et réactifs; Energie électrique; Thermique [physics.class-ph]; Vibrations [physics.class-ph]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]; Acoustique [physics.class-ph]; Biomécanique [physics.med-ph]; Matériaux; Polymères

Azdine Nait- Ali. Stochastic homogenization of reinforced polymer with very small carbon inclusions. Comptes Rendus Mécanique, 2018, 346 (12), pp.1192-1198. ⟨10.1016/j.crme.2018.09.002⟩. ⟨hal-02318878⟩