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.

翻译：本文研究了Hornung、Neukamm与Velčić于2014年提出的微结构薄板弹性变形均质化降维模型的离散化问题。其中，非线性弯曲能量基于作用于弹性变形第二基本形式的均质化二次型。对涉及的三维微观胞元问题采用多仿射有限元离散，对受等距约束的二维宏观问题采用离散基尔霍夫三角形离散，并证明了收敛性。最后，通过选取的数值算例验证了收敛特性，并与微结构纸板的变形实验进行了定性比较。