The effect of plasticity in crumpling of thin sheets

Abstract

Crumpling a thin sheet of material into a small volume requires energy for creating a network of deformations such as vertices and ridges. Scaling properties of a single elastic vertex or ridge have been analysed theoretically, and crumpling of a sheet by numerical simulations. Real materials are however elasto-plastic and large local strains induce irreversible plastic deformations. Hence, a numerical model that can be purely elastic or elasto-plastic is introduced. In crumpled elastic sheets, the ridge patterns are found to be similar, independent of the width to thickness (L/h) ratio of the sheet, and the fractal dimension of crumpled sheets is given by scaling properties of the energy and average length of ridges. In crumpled elasto-plastic sheets, such a similarity does not appear as the L/h ratio affects the deformations, and the fractal dimension (Dpl) is thereby reduced. Evidence is also found of Dpl not being universal but dependent on the plastic yield point of the material.