Two-Scale Finite Element Approximation of a Homogenized Plate Model
Abstract
This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Vel\v{c}i\'c in 2014. Thereby, a nonlinear bending energy is based on a homogenized quadratic form which acts on the second fundamental form associated with the elastic deformation. Convergence is proven for a multi-affine finite element discretization of the involved three-dimensional microscopic cell problems and a discrete Kirchhoff triangle discretization of the two-dimensional isometry-constrained macroscopic problem. Finally, the convergence properties are numerically verified in selected test cases and qualitatively compared with deformation experiments for microstructured sheets of paper.
Keywords
Cite
@article{arxiv.2308.14431,
title = {Two-Scale Finite Element Approximation of a Homogenized Plate Model},
author = {Martin Rumpf and Stefan Simon and Christoph Smoch},
journal= {arXiv preprint arXiv:2308.14431},
year = {2024}
}