Bilayer plates are compound materials that exhibit large bending deformations when exposed to environmental changes that lead to different mechanical responses in the involved materials. In this article a new numerical method that is suitable for simulating the isometric deformation induced by a given material mismatch in a bilayer plate is discussed. A dimensionally reduced formulation of the bending energy is discretized generically in an abstract setting and specified for discrete Kirchhoff triangles; convergence towards the continuous formulation is proved. A practical semi-implicit discrete gradient flow employing a linearization of the isometry constraint is proposed as an iterative method for the minimization of the bending energy; stability and a bound on the violation of the isometry constraint are proved. The incorporation of obstacles is discussed and the practical performance of the method is illustrated with numerical experiments involving the simulation of large bending deformations and investigation of contact phenomena.

中文翻译：

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用于模拟具有等距和障碍物约束的双层板弯曲的稳定梯度流离散化

双层板是复合材料，当暴露于环境变化时会表现出较大的弯曲变形，从而导致相关材料产生不同的机械响应。本文讨论了一种适用于模拟双层板中给定材料失配引起的等距变形的新数值方法。弯曲能量的降维公式通常在抽象设置中离散化，并为离散的基尔霍夫三角形指定；证明了对连续公式的收敛性。提出了一种采用等距约束线性化的实用半隐式离散梯度流作为最小化弯曲能量的迭代方法；证明了稳定性和违反等距约束的界限。