Derivation of a homogenized nonlinear plate theory from 3d elasticity

2012/10/19 by Hornung, Peter, Neukamm, Stefan, Velcic, Igor
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1210.5461

Abstract

We derive, via simultaneous homogenization and dimension reduction, the Gamma-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the energy scaling that corresponds to Kirchhoff's nonlinear bending theory of plates.

Related

• On the derivation of homogenized bending plate model
• On the general homogenization of von Karman plate equations from 3D nonlinear elasticity
• A hierarchy of multilayered plate models
• Homogenization of bending theory for plates; the case of elastic laminates
• Shell theories arising as low energy Γ-limit of 3d nonlinear elasticity