Power law scaling of lateral deformations with universal Poisson's index for randomly folded thin sheets

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of paper obey a power law behavior with the universal Poisson's index ν=0.17±0.01, which does not depend neither the paper kind and sheet sizes (thickness, edge length) nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poisson's ratio νe =0.33±0.01. This difference is consistent with the difference in fractal topology of randomly folded elastoplastic and predominantly plastic sheets, which is found to belong to different universality classes. The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested.