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Publication 15-CNA-001

Multiscale Homogenization in Kirchhoff's Nonlinear Plate Theory

Laura Bufford
Department of Mathematical Sciences
Carnegie Mellon University, Pittsburgh, PA 15213, USA
lbufford@andrew.cmu.edu

Elisa Davoli
Department of Mathematical Sciences
Carnegie Mellon University, Pittsburgh, PA 15213, USA
edavoli@andrew.cmu.edu

Irene Fonseca
Center for Nonlinear Analysis
Department of Mathematical Sciences
Carnegie Mellon University, Pittsburgh, PA 15213, USA
fonseca@andrew.cmu.edu

Abstract: The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff's non- linear bending theory for plates. Di fferent limit models are deduced depending on the relative ratio between the thickness parameter $h$ and the two homogenization scales $\epsilon$ and $\epsilon^2$.

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