The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling conditions on the energy and the geometric properties of the folding arc in dependence on the small sheet thickness. The resulting two-dimensional model is a piecewise nonlinear Kirchhoff plate bending model with a continuity condition at the folding arc. A discontinuous Galerkin method and an iterative scheme are devised for the accurate numerical approximation of large deformations.

翻译：文章用数学模型将薄弹性板折叠成一个指定的弯曲弧。一般超弹性材料描述的严格模型削减是在对小厚厚度依赖的折叠弧的能量和几何特性的适当缩放条件下进行的。由此形成的二维模型是一块非线性非Kirchhoff板弯曲模型,在折叠弧上具有连续性条件。为了大变形的准确数字近似,设计了一个不连续的加勒金方法和一个迭接方案。