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Asymptotic analysis for domains separated by a thin layer made of periodic vertical beams

: Griso, G.; Migunova, Anastasia; Orlik, Julia


Journal of elasticity 128 (2017), No.2, pp.291-331
ISSN: 0374-3535 (Print)
ISSN: 1573-2681 (Online)
Journal Article
Fraunhofer ITWM ()
junction between two 3D domains and beam; linear elasticity decomposition of beam displacements; homogenization

We consider a thin heterogeneous layer consisting of thin beams (of radius r)and study the limit behavior of this problem as the period ε, the thickness δ and the radius r of the beams tend to zero. The decomposition of the displacement field into beams developed by Griso (J. Math. Pures Appl. 89:199223, 2008) is used, which allows to obtain a priori estimates. Two types of unfolding operators are introduced to deal with different parts of the decomposition. In conclusion, we obtain the limit problem together with transmission conditions across the interface.