The effect of plasticity in crumpling of thin sheets

Crumpling a thin sheet of material into a small volume requires energy for creating a network of deformations such as vertices and ridges(1,2). Scaling properties of a single elastic vertex(3-5) or ridge have been analysed theoretically(6-8), and crumpling of a sheet by numerical simulations(1,9,10). Real materials are however elasto-plastic(11-15) 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 (D-pl) is thereby reduced. Evidence is also found of D-pl not being universal but dependent on the plastic yield point of the material.