Derivation of the homogenized von K´arm´an plate theory from 3d elasticity

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung


  • Stefan Neukamm - , Max Planck Institute for Mathematics in the Sciences (Autor:in)
  • Igor Velcic - , University of Zagreb (Autor:in)


We rigorously derive a homogenized von-Karman plate theory as a G-limit from nonlinear three-dimensional elasticity by combining homogenization and dimension reduction. Our starting point is an energy functional that describes a nonlinear elastic, threedimensional plate with spatially periodic material properties. The functional features two small length scales: the period e of the elastic composite material, and the thickness h of the slender plate. We study the behavior as e and h simultaneously converge to zero in the von-Karman scaling regime. The obtained limit is a homogenized von-Karman plate model. Its effective material properties are determined by a relaxation formula that exposes a non-trivial coupling of the behavior of the out-of-plane displacement with the oscillatory behavior in the in-plane directions. In particular, the homogenized coefficients depend on the relative scaling between h and epsilon, and different values arise for h << epsilon, epsilon similar to h and epsilon << h.


Seiten (von - bis)2701-2748
FachzeitschriftMathematical Models and Methods in Applied Sciences
PublikationsstatusVeröffentlicht - Dez. 2013
Extern publiziertJa

Externe IDs

Scopus 84885639972



  • Elasticity, dimension reduction, homogenization, von-Karman plate theory, two-scale convergence, DOUBLE-POROSITY MODEL, INTEGRAL FUNCTIONALS, 2-SCALE CONVERGENCE, GAMMA-CONVERGENCE, FLOW