Fractal Geometry and Mechanics of Randomly Folded Thin Sheets

Abstract

This work is devoted to the statistical geometry of crumpling network and its effect on the geometry and mechanical properties of randomly folded materials. We found that crumpling networks in randomly folded sheets of different kinds of paper exhibit statistical self-similarity characterized by the universal fractal dimension DN = 1.83 ± 0.03. The balance of bending and stretching energy stored in the folded creases determines the fractal geometry of folded sheets displaying intrinsically anomalous self-similarity with the universal local fractal dimension Dl = 2.67 ± 0.05 and the material dependent global fractal dimension D < Dl. Moreover, we found that the entropic rigidity of crumpling network governs the mechanical behavior of randomly crumpled sheets under uniaxial compression.