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arXiv · 2308.14431

Two-Scale Finite Element Approximation of a Homogenized Plate Model

Martin Rumpf·Stefan Simon·Christoph Smoch
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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.

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Martin Rumpf, Stefan Simon, Christoph Smoch. 2023-08-28. Two-Scale Finite Element Approximation of a Homogenized Plate Model. https://arxiv.org/abs/2308.14431

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