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, we adopt two different formulations of the governing equations of motion: a quasistatic formulation that effectively describes smooth deformations, and a fully dynamic formulation that captures large changes in the sheet's velocity. The former is a differential-algebraic system solved implicitly, while the latter is a purely differential system solved explicitly, using a hybrid integration scheme that adaptively alternates between the two representations. 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:在这项工作中,我们提出了一个模拟大规模变形和变形的薄薄弹性板的方法。受薄薄薄薄片在翻滚过程中的实际行为的驱使,我们采用了两种不同的运动方程式:一种有效描述平滑变形的准静态配方,一种完全动态的配方,捕捉工作表速度的重大变化。前者是一个隐蔽地解决差异-热层系统,而后者则是一个纯粹的分化系统,它使用一种混合集成计划,在两个代表体之间进行适应性交替。我们展示了这种方法有效模拟各种折叠现象的能力。最后,我们表明统计特性,特别是反复加载的裂缝的积累,以及方块的分布,与实验性观察是一致的。