  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 Poissons index nu
= 0.17 pm 0.01, which does not depend neither the paper kind and sheet sizes,
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 Poissons
ratio nu_e = 0.33 pm 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.
