Bilayer plates are slender structures made of two thin layers of different materials. They react to environmental stimuli and undergo large bending deformations with relatively small actuation. The reduced model is a constrained minimization problem for the second fundamental form, with a given spontaneous curvature that encodes material properties, subject to an isometry constraint. We design a local discontinuous Galerkin (LDG) method which imposes a relaxed discrete isometry constraint and controls deformation gradients at barycenters of elements. We prove $\Gamma$-convergence of LDG, design a fully practical gradient flow, which gives rise to a linear scheme at every step, and show energy stability and control of the isometry defect. We extend the $\Gamma$-convergence analysis to piecewise quadratic creases. We also illustrate the performance of the LDG method with several insightful simulations of large deformations, one including a curved crease.

翻译：双层板是由两种不同材料的薄层组成的细长结构。它们对环境刺激作出反应，并以相对较小的驱动产生大弯曲变形。简化模型是关于第二基本形式的约束极小化问题，其中给定编码材料特性的自发曲率，并受等距约束。我们设计了一种局部间断伽辽金（LDG）方法，该方法施加松弛的离散等距约束，并在单元重心处控制变形梯度。我们证明了LDG的$\Gamma$-收敛性，设计了一种完全实用的梯度流（每步产生线性格式），并展示了能量稳定性和等距缺陷的控制。我们将$\Gamma$-收敛分析推广到分段二次折痕。我们还通过几个具有洞察力的大变形模拟（包括一个包含弯曲折痕的模拟）展示了LDG方法的性能。