# Science at the triple point between mathematics, mechanics and materials science

## Publication 116

### Multiscale Homogenization in Kirchhoff's Nonlinear Plate Theory

##### Authors:

Laura Bufford
Department of Mathematical Sciences
Carnegie Mellon University, Pittsburgh, PA 15213, USA

Elisa Davoli
Department of Mathematical Sciences
Carnegie Mellon University Pittsburgh, PA 15213

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

##### 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. Different limit models are deduced depending on the relative ratio between the thickness parameter $h$ and the two homogenization scales $\epsilon$ and $\epsilon^2$.
##### Get the paper in its entirety
15-CNA-001.pdf

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