Fractal Geometry and Mechanics of Randomly Folded Thin Sheets

  • Alexander S. Balankin
  • Orlando Susarrey Huerta
Conference paper
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)


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.


Folded matter fractal scaling mechanical properties 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Alexander S. Balankin
    • 1
  • Orlando Susarrey Huerta
  1. 1.Instituto Politécnico Nacional Ed. 5, 3piso, ESIMEAv. Politecnico NacionalMexico

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