  We have studied experimentally and theoretically the response of randomly
folded hyperelastic and elastoplastic sheets on the uniaxial compression
loading and the statistical properties of crumpling networks. The results of
these studies reveal that the mechanical behavior of randomly folded sheets in
the one-dimensional stress state is governed by the shape dependence of the
crumpling network entropy. Following up on the original ideas by Edwards for
granular materials, we derive an explicit force-compression relationship which
precisely fits the experimental data for randomly folded matter. Experimental
data also indicate that the entropic rigidity modulus scales as the power of
the mass density of the folded ball with universal scaling exponent.
