On the general homogenization and Γ-closure for the equations of von Kármán plate from 3D nonlinear elasticity

Igor Velčić

Contact the author: Please use for correspondence this email.
Submission date: 26. Jun. 2013 (revised version: July 2013)
Pages: 54
published in: Analysis and applications, 15 (2017) 1, p. 1-49 
DOI number (of the published article): 10.1142/S0219530515500244
Bibtex
with the following different title: On the general homogenization of von Kármán plate equations from three-dimensional nonlinear elasticity
MSC-Numbers: 35B2, 74Q15, 74K20
Keywords and phrases: elasticity, dimension reduction, homogenization, von K\'arm\'an plate model
Download full preprint: PDF (526 kB)

Abstract:
Starting from 3D elasticity equations we derive the model of the homogenized von Kármán plate by means of Γ-convergence. This generalizes the recent results, where the material oscillations were assumed to be periodic. We also prove the locality of Γ-closure i.e. that every energy density obtained in this way by mixing n different materials is at almost every point of domain limit of some sequence of the energy densities obtained by periodic homogenization.