Two-Scale Finite Element Approximation of a Homogenized Plate Model

2023/08/28 by Rumpf, Martin, Simon, Stefan, Smoch, Christoph · 1 citation
#65N12 #65N30 #74E25 #74K20 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2308.14431

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 Velčić 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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• Finite element discretizations of bending plates with prestrained microstructure

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