A numerical scheme is proposed to identify low energy configurations of a F\"oppl-von K\'arm\'an model for bilayer plates. The dependency of the corresponding elastic energy on the in-plane displacement $u$ and the out-of-plane deflection $w$ leads to a practical minimization of the functional via a decoupled gradient flow. In particular, the energies of the resulting iterates are shown to be monotonically decreasing. The discretization of the model relies on $P1$ finite elements for the horizontal part $u$ and utilizes the discrete Kirchhoff triangle for the vertical component $w$. The model allows for analysing various different problem settings via numerical simulation: (i) stable low-energy configurations are detected dependent on a specified prestrain described by elastic material properties, (ii) curvature inversions of spherical and cylindrical configurations are investigated, (iii) elastic responses of foldable cardboards for different spontaneous curvatures and crease geometries are compared.

翻译：本文提出了一种数值方案，用于识别双层板Föppl-von Kármán模型的低能量构型。该模型弹性能量对平面内位移$u$与面外挠度$w$的依赖性，通过解耦梯度流实现了泛函的实际最小化。特别地，证明了所得迭代序列的能量具有单调递减性。模型的离散化采用$P1$有限元处理水平分量$u$，并运用离散Kirchhoff三角形单元处理垂直分量$w$。该模型可通过数值模拟分析多种不同问题设置：（i）依据由弹性材料属性描述的特定预应变检测稳定的低能量构型；（ii）研究球面与柱面构型的曲率反转现象；（iii）比较具有不同自发曲率与折痕几何的可折叠纸板的弹性响应。