A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the second fundamental form of the middle plate and the latter is a restriction on its first fundamental form. We discuss a formal derivation of this reduced model along with an equivalent formulation that makes it amenable computationally. We propose a local discontinuous Galerkin (LDG) finite element approach that hinges on the notion of reconstructed Hessian. We design discrete gradient flows to minimize the ensuing nonconvex problem and to find a suitable initial deformation. We present several insightful numerical experiments, some of practical interest, and assess various computational aspects of the approximation process.

预应变板大变形的简化模型包括最小化受非凸度量约束的二阶弯曲能量。前者涉及中板的第二种基本形式，后者是对其第一种基本形式的限制。我们讨论了这个简化模型的形式推导以及使其在计算上适用的等效公式。我们提出了一种基于重建 Hessian 概念的局部不连续伽辽金 (LDG) 有限元方法。我们设计离散梯度流以最小化随之而来的非凸问题并找到合适的初始变形。我们提出了几个有见地的数值实验，一些具有实际意义的实验，并评估了近似过程的各种计算方面。