双层板：模型降阶、Γ-收敛有限元近似与离散梯度流
Bilayer Plates: Model Reduction, $Γ$-Convergent Finite Element Approximation and Discrete Gradient Flow
AI总结：
本文研究双层板的弯曲机制，通过小的外部诱导晶格不匹配实现大变形，提出基于Kirchhoff四边形的离散化方法，并证明其Γ-收敛性，通过数值实验验证了能量下降迭代方法的收敛性和降阶模型的性能。
摘要：
双层板的弯曲机制通过小的外部诱导晶格不匹配实现大变形，其数学建模为一个非线性四阶问题，包含点wise等距约束。本文提出基于Kirchhoff四边形的离散化方法，并证明其Γ-收敛性。提出一种能量下降迭代方法，并研究其收敛到稳定配置的过程。通过多个数值实验探讨了该方法的性能及降阶模型的能力，涉及大变形（几何非线性）情况。
英文摘要：
The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order problem with a pointwise isometry constraint. A discretization based on Kirchhoff quadrilaterals is devised and its $Γ$-convergence is proved. An iterative method that decreases the energy is proposed and its convergence to stationary configurations is investigated. Its performance, as well as reduced model capabilities, are explored via several insightful numerical experiments involving large (geometrically nonlinear) deformations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
