In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, two different formulations of the governing equations of motion are used: (1) a quasistatic formulation that effectively describes smooth deformations, and (2) a fully dynamic formulation that captures large changes in the sheet's velocity. The former is a differential-algebraic system of equations integrated implicitly in time, while the latter is a set of ordinary differential equations (ODEs) integrated explicitly. We adopt a hybrid integration scheme to adaptively alternate between the quasistatic and dynamic representations as appropriate. We demonstrate the capacity of this method to effectively simulate a variety of crumpling phenomena. Finally, we show that statistical properties, notably the accumulation of creases under repeated loading, as well as the area distribution of facets, are consistent with experimental observations.

翻译：本文提出了一种模拟薄弹塑性片材大尺度变形与褶皱过程的方法。受薄片在褶皱过程中物理行为的启发，我们采用了两种不同的运动控制方程形式：（1）准静态形式，有效描述平滑变形；（2）全动态形式，捕捉片材速度的剧烈变化。前者为隐式时间积分的微分代数方程组，后者为显式积分的常微分方程组。我们采用混合积分方案，根据实际情况自适应交替使用准静态与动态表征。实验证明该方法能有效模拟多种褶皱现象。最后，我们证明统计数据——特别是重复加载下的折痕累积及面片面积分布——与实验观测结果一致。