Simulation of crumpled sheets via alternating quasistatic and dynamic representations

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.