A note on the derivation of homogenized bending plate model
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Submission date: 14. Mar. 2013
published in: Calculus of variations and partial differential equations, 53 (2015) 3-4, p. 561-586
DOI number (of the published article): 10.1007/s00526-014-0758-1
MSC-Numbers: 35B27, 49J4, 74E30, 74Q05, 74Q20
Keywords and phrases: elasticity, dimension reduction, homogenization, nonlinear plate theory, two-scale convergence
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We derive, via simultaneous homogenization and dimension reduction, the Γ-limit for thin elastic plates of thickness h whose energy density oscillates on a scale ϵ(h) such that ϵ(h)2 ≪ h ≪ ϵ(h). We consider the energy scaling that corresponds to Kirchhoff’s nonlinear bending theory of plates.