In [Bonito et al., J. Comput. Phys. (2022)], a local discontinous Galerkin method was proposed for approximating the large bending of prestrained plates, and in [Bonito et al., IMA J. Numer. Anal. (2023)] the numerical properties of this method were explored. These works considered deformations driven predominantly by bending. Thus, a bending energy with a metric constraint was considered. We extend these results to the case of an energy with both a bending component and a nonconvex stretching component, and we also consider folding across a crease. The proposed discretization of this energy features a continuous finite element space, as well as a discrete Hessian operator. We establish the $\Gamma$-convergence of the discrete to the continuous energy and also present an energy-decreasing gradient flow for finding critical points of the discrete energy. Finally, we provide numerical simulations illustrating the convergence of minimizers and the capabilities of the model.

翻译：在[Bonito等人，《计算物理学杂志》(2022)]中，提出了一种局部间断伽辽金方法用于近似预应变板的大弯曲变形，随后[Bonito等人，《IMA数值分析杂志》(2023)]探讨了该方法的数值性质。这些工作主要考虑由弯曲主导的变形，因此采用了带有度量约束的弯曲能。我们将这些结果推广至同时包含弯曲分量和非凸拉伸分量的能量情形，并进一步考虑沿折痕的折叠行为。所提出的能量离散化方案采用了连续有限元空间及离散海森算子。我们建立了离散能量到连续能量的Γ-收敛性，并提出了一种能量递减梯度流以寻找离散能量的临界点。最后通过数值模拟展示了极小化子的收敛性及模型能力。