Remark on the Homogenization of a Micro-fibered Linearly Elastic Material

Somsak Orankitjaroen (1) , Nuttawat Sontichai (2) , Christian Licht (3) , Amnuay Kananthai (4)

1 Department of Mathematics
2 Department of Mathematics
3 M3 - Modélisation Mathématique en Mécanique
4 Departments of Mathematics

We consider the homogenization of a linear elliptic boundary value problem of elasticity. The isotropic elastic material is reinforced by a periodic distribution of very thin parallel fibers in which the Lamé coefficients are assumed to have high values. Bellieud and Gruais proved that the macroscopic behavior is the one of a generalized continuum medium involving an additional state variable accounting for the microstructure. Here we propose a proof of this result by studying the variational convergence of the energy functional.

Mots clés: homogenization; variational convergence; capacitary problems

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Somsak Orankitjaroen, Nuttawat Sontichai, Christian Licht, Amnuay Kananthai. Remark on the Homogenization of a Micro-fibered Linearly Elastic Material. International Conference on Mathematics and Applications, ICMA-MU 2009, Dec 2009, Thailand. pp.153-165. ⟨hal-00747037⟩