We discuss spontaneously bent configurations of pre-stretched bilayer sheets that can be obtained by tuning the pre-stretches in the two layers. The two-dimensional nonlinear plate model we use for this purpose is an adaptation of the one recently obtained for thin sheets of nematic elastomers, by means of a rigorous dimensional reduction argument based on the theory of Gamma-convergence (Agostiniani and DeSimone in Meccanica. doi:10.1007/s11012-017-0630-4, 2017, Math Mech Solids. doi:10.1177/1081286517699991, arXiv:1509.07003, 2017). We argue that pre-stretched bilayer sheets provide us with an interesting model system to study shape programming and morphing of surfaces in other, more complex systems, where spontaneous deformations are induced by swelling due to the absorption of a liquid, phase transformations, thermal or electro-magnetic stimuli. These include bio-mimetic structures inspired by biological systems from both the plant and the animal kingdoms.

中文翻译：

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预拉伸双层的自发弯曲

我们讨论了可以通过调整两层中的预拉伸来获得的预拉伸双层片材的自发弯曲配置。我们为此目的使用的二维非线性板模型是对最近获得的向列弹性体薄片模型的改编，通过基于伽马收敛理论的严格的降维论证（Agostiniani 和 DeSimone in Meccanica. doi:10.1007/s11012-017-0630-4, 2017, Math Mech Solids.doi:10.1177/1081286517699991, arXiv:1509.07003, 2017)。我们认为，预拉伸双层片材为我们提供了一个有趣的模型系统，用于研究其他更复杂系统中的形状编程和表面变形，其中由于吸收液体、相变、膨胀引起自发变形，热或电磁刺激。其中包括受植物和动物王国生物系统启发的仿生结构。