We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint. Equilibrium deformations are approximated using local discontinuous Galerkin (LDG) finite elements. The design of the discrete energies relies on a discrete Hessian operator defined on discontinuous functions with better approximation properties than the piecewise Hessian. Discrete gradient flows are put in place to drive the minimization process. They are chosen for their robustness and ability to preserve the nonconvex constraint. Several numerical experiments are presented to showcase the large variety of shapes that can be achieved with these models.

翻译：本文综述了以弯曲为主要机制实现大变形的薄结构（约化）模型。每个模型均涉及四阶能量极小化问题，且可能需满足非凸约束条件。采用局部间断伽辽金（LDG）有限元法对平衡变形进行数值逼近。离散能量的构造基于定义在间断函数上的离散黑塞算子，该算子具有比逐段黑塞算子更优异的逼近特性。通过构建离散梯度流驱动极小化过程，该方法因其鲁棒性及保持非凸约束的能力而被采用。数值实验展示了该类模型可生成的丰富形状。