Homogenization of perforated elastic structures

Georges Griso (1) , Larysa Khilkova (2) , Julia Orlik (2) , Olena Sivak (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Fraunhofer ITWM - Fraunhofer Institute of Industrial Mathematics

The paper is dedicated to the asymptotic behavior of periodically perforated elastic domains (3D, plate-like or beam-like). We homogenize these structures, passing to the limit w.r.t. the period. In case of plate-like or beam-like structures we simultaneously proceed to a dimension reduction. These periodic structures can be made e.g. of balls or cylinders glued, so that the surface in contact has a non-zero measure. Since the boundaries of these structures might be non-Lipschitz, the classical extension approach does not serve. We will proceed using interpolations. The Korn inequalities in the case of thin structures are based on the decomposition of beam or plate displacements. For the asymptotic behavior the unfolding and rescaling operators are used.

Mots clés: Keyword: Homogenization; periodic unfolding method; dimension reduction; linear elasticity; variational inequal- ity; perforated non-Lipschitz domains; plates; beams; extension operators and Korn inequalities 35B27

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Georges Griso, Larysa Khilkova, Julia Orlik, Olena Sivak. Homogenization of perforated elastic structures. 2019. ⟨hal-02279709⟩