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.
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References
Wood AJ, “Witten’s Lectures on Crumpling”, Physica A, 313, pp. 83–109, 2002.
Kramer EM, Witten TA, “Stress Condensation in Crushed Elastic Manifolds”, Physical Review Letters, 78, pp. 13083–1306, 1997.
DiDonna BA, Witten TA, “Anomalous Strength of Membranes with Elastic Ridges”, Physical Review Letters, 87, pp. 2061051–2061054, 2001.
Matan K, Williams RB, Witten TA, Nagel SR, “Crumpling a Thin Sheet”, Physical Review Letters, 88, pp. 0761011–0761014, 2002.
Astrom JA, Timonen J., Karttunen M, “Crumpling of a Stiff Tethered Membrane”, Physical Review Letters, 93, pp. 2443011–2443014, 2004.
Blair DL, Kudrolli A, “Geometry of Crumpled Paper”, Physical Review Letters, 94, pp. 1661071–1661074, 2005.
Sultan E, Boudaoud A, “Statistics of Crumpled Paper”, Physical Review Letters, 96, pp. 1361031–1361034, 2006.
Vliegenthart GA, Gompper G, “Forced Crumpling of Self-avoiding Elastic Sheets”, Nature Materials, 96, pp. 1361031–1361034, 2006.
Balankin AS, Morales D, Susarrey O, Samayoa D, Trinidad JM, Marquez J, García R, “Self-Similar Roughening of Drying Wet Paper”, Physical Review E, 73, pp. 0651051–0651054, 2006.
Balankin AS, Susarrey O, Cortes R, Samayoa D, Trinidad JM, Mendoza MA, “Intrinsically Anomalous Roughness of Randomly Crumpled Thin Sheets”, Physical Review E, 74, pp. 061601–061607, 2006.
Balankin AS, Campos I, Martínez OA, Susarrey O, “Scaling Properties of Randomly Folded Plastic Sheets”, Physical Review E, 75, pp. 0511171–0511173, 2007.
Balankin AS, Cortes R, Samayoa D, “Intrinsically Anomalous Self-Similarity of Randomly Folded Matter”, Physical Review E, 76, 0321011–0321014, 2007.
Gompper G, “Patterns of Stress in Crumpled Sheets” Nature, 386, pp. 439–441, 1997.
Albuquerque AJ, Gomez MAF, “Stress Relaxation in Crumpled Surfaces”, Physica A, 310, pp. 377–383, 2002.
Bowick MJ, Travesset A, “The Statistical Mechanics of Membranes”, Physics Reports, 344, pp. 255–308, 2001.
Ramasco JJ, López JM, Rodríguez MA, “Generic Dynamic Scaling in Kinetic Roughening”, Physical Review Letters, 84, pp. 2199–2202, 2000.
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Balankin, A.S., Huerta, O.S. (2009). Fractal Geometry and Mechanics of Randomly Folded Thin Sheets. In: Borodich, F. (eds) IUTAM Symposium on Scaling in Solid Mechanics. Iutam Bookseries, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9033-2_22
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DOI: https://doi.org/10.1007/978-1-4020-9033-2_22
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