Entropic rigidity of a crumpling network in a randomly folded thin sheet

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 5, 2008, Pages

  Balankin, Alexander S ^a   Huerta, Orlando Susarrey ^a  

^a INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTICITY; GRANULAR MATERIALS; LOADS (FORCES); STRESS ANALYSIS;

ELASTOPLASTIC SHEETS; HYPERELASTIC;

SHEET METAL;

EID: 44449120460     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.051124     Document Type: Article

References (87)

1. R. Lipowsky, Nature (London) NATUAS 0028-0836 10.1038/349475a0 349, 475 (1991).
2. M. J. Bowick and A. Travesset, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00128-9 344, 255 (2001).
3. A. J. Wood, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)01260-8 313, 83 (2002).
4. T. A. Witten, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/17/20/001 17, S1651 (2005).
5. T. A. Witten, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.79.643 79, 643 (2007).
6. G. Gompper, Nature (London) NATUAS 0028-0836 10.1038/386439a0 386, 439 (1997).
7. T. Haliloglu, I. Bahar, and B. Erman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3090 79, 3090 (1997).
8. M. Ben Amar and Y. Pomeau, Proc. R. Soc. London, Ser. A PRLAAZ 0950-1207 10.1098/rspa.1997.0041 453, 729 (1997).
9. E. M. Kramer and T. A. Witten, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.1303 78, 1303 (1997).
10. E. Cerda and L. Mahadevan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2358 80, 2358 (1998)
11. E. Cerda and L. Mahadevan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.074302 90, 074302 (2003).
12. E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, Nature (London) NATUAS 0028-0836 10.1038/43395 401, 46 (1999).
13. A. Boudaoud, P. Patrício, Y. Couder, and M. Ben Amar, Nature (London) NATUAS 0028-0836 10.1038/35037535 407, 718 (2000).
14. R. Lakes, Nature (London) NATUAS 0028-0836 10.1038/35107190 414, 503 (2001).
15. R. K. Lambert, P. D. ParÁ, and M. Okazawa, J. Appl. Physiol. 90, 2041 (2001). 0021-8987
16. B. A. DiDonna and T. A. Witten, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.206105 87, 206105 (2001).
17. B. A. DiDonna, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.016601 66, 016601 (2002).
18. K. Matan, R. B. Williams, T. A. Witten, and S. R. Nagel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.076101 88, 076101 (2002).
19. R. F. Albuquerque and M. A. F. Gomes, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)00747-1 310, 377 (2002).
20. E. M. Arkin, S. P. Fekete, and J. S. B. Mitchell, Comput. Geom. 25, 117 (2003). 0925-7721
21. F. Rao and A. Caflisch, J. Mol. Biol. JMOBAK 0022-2836 10.1016/j.jmb.2004.06.063 342, 299 (2004).
22. J. A. Astrom, J. Timonen, and M. Karttunen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.244301 93, 244301 (2004).
23. P. F. N. Faisca, M. M. Telo da Gama, and R. C. Ball, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.051917 69, 051917 (2004).
24. L. Bevilacqua, Appl. Math. Model. AMMODL 0307-904X 10.1016/j.apm.2003.10. 017 28, 547 (2004).
25. L. Qiu and S. J. Hagen, Chem. Phys. CMPHC2 0301-0104 10.1016/j.chemphys. 2004.12.002 312, 327 (2005).
26. D. L. Blair and T. A. Kudrolli, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.166107 94, 166107 (2005).
27. S. Conti, A. DeSimone, and S. Muller, Comput. Methods Appl. Mech. Eng. CMMECC 0045-7825 10.1016/j.cma.2004.07.044 194, 2534 (2005).
28. T. Liang and T. A. Witten, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.016612 71, 016612 (2005).
29. P. B. Noble, A. Sharma, P. K. McFawn, and H. W. Mitchell, J. Appl. Physiol. JAPHEV 8750-7587 10.1152/japplphysiol.00485.2005 99, 2061 (2005).
30. S. Chaieb, V. K. Natrajan, and A. A. El-Rahman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.078101 96, 078101 (2006).
31. E. Sultan and A. Boudaoud, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.136103 96, 136103 (2006).
32. E. Katzav, M. Adda-Bedia, and A. Boudaoud, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0609079103 103, 18900 (2006).
33. G. A. Vliegenthart and G. Gompper, Nat. Mater. NMAACR 1476-1122 10.1038/nmat1581 5, 216 (2006).
34. G. A. Vliegenthart and G. Gompper, Biophys. J. BIOJAU 0006-3495 10.1529/biophysj.106.081422 91, 834 (2006).
35. R. Twarock, Philos. Trans. R. Soc. London, Ser. A PTRMAD 0962-8428 10.1098/rsta.2006.1900 364, 3357 (2006).
36. R. Cassia-Moura and M. A. F. Gomes, J. Theor. Biol. 238, 331 (2006). 0022-5193
37. A. S. Balankin, D. Morales, O. Susarrey, D. Samayoa, J. Martínez, and M. A. Mendoza, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.065105 73, 065105 (R) (2006).
38. A. S. Balankin, O. Susarrey, R. C. Montes de Oca, D. Samayoa, J. Martínez, J. Marquez, and R. García, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.061602 74, 061602 (2006).
39. M. A. F. Gomes, C. C. Donato, S. L. Campello, R. E. De Souza, and R. Cassia-Moura, J. Phys. D JPAPBE 0022-3727 10.1088/0022-3727/40/12/017 40, 3665 (2007).
40. C. C. Donato and M. A. F. Gomes, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.066113 75, 066113 (2007).
41. H. Koibuchi, J. Stat. Phys. 127, 457 (2007). 0022-4715
42. E. Sharon, B. Roman, and H. L. Swinney, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.046211 75, 046211 (2007).
43. A. S. Balankin, I. Campos, O. A. Martínez, and O. Susarrey, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.051117 75, 051117 (2007).
44. A. S. Balankin, R. C. Montes de Oca, and D. Samayoa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.032101 76, 032101 (2007).
45. Ch. A. Andresen, A. Hansen, and J. Schmittbuhl, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.026108 76, 026108 (2007).
46. L. BouÁ and E. Katzav, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/80/54002 80, 54002 (2007).
47. M. El-Ghoul, Chaos Solitons Fractals 12, 1019 (2001). 0960-0779
48. M. A. F. Gomes and V. M. Oliveira, Philos. Mag. Lett. PMLEEG 0950-0839 10.1080/095008398177913 78, 325 (1998).
49. A. Lobkovsky, Sh. Gentges, H. Li, D. Morse, and T. A. Witten, Science SCIEAS 0036-8075 10.1126/science.270.5241.1482 270, 1482 (1995).
50. T. A. Witten and H. Li, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/23/1/009 23, 51 (1993).
51. A. Lobkovsky, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.3750 53, 3750 (1996).
52. M. A. F. Gomes, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.15094 55, 649 (1987).
53. M. A. F. Gomes, G. L. Vasconcelos, and C. C. Nascimento, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/20/17/007 20, L1167 (1987).
54. M. A. F. Gomes, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/20/5/005 20, L283 (1987).
55. M. A. F. Gomes, I. J. C. Braga, and C. A. F. Castro, J. Phys. A 22, 1463 (1989). 0022-3689
56. M. A. F. Gomes, T. I. Lyh, and T. I. Ren, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/23/24/001 23, L1281 (1990).
57. J. B. C. Garcia, M. A. F. Gomes, T. I. Lyh, and T. I. Ren, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/25/7/012 25, L353 (1992).
58. M. A. F. Gomes and J. H. P. Soares, J. Phys. D JPAPBE 0022-3727 10.1088/0022-3727/22/7/019 22, 989 (1989).
59. M. A. F. Gomes, T. I. Lyh, T. I. Ren, I. M. Rodrigues, and C. B. S. Furtado, J. Phys. D JPAPBE 0022-3727 10.1088/0022-3727/22/8/030 22, 1217 (1989).
60. J. Weiner, Statistical Mechanics of Elasticity (Wiley, New York, 1983).
61. A. S. Balankin, D. Samayoa, E. Pineda, R. C. Montes de Oca, A. Horta, and M. A. Martínez, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.125421 77, 125421 (2008).
62. M. L. Gardel, J. H. Shin, F. C. MacKintosh, L. Mahadevan, P. Matsudaira, and D. A. Weitz, Science SCIEAS 0036-8075 10.1126/science.1095087 304, 1301 (2004).
63. Y. Kantor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.39.6582 39, 6582 (1989)
64. E. Duering and Y. Kantor, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.7443 40, 7443 (1989)
65. O. Farago and Y. Kantor, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.2533 85, 2533 (2000)
66. O. Farago and Y. Kantor, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.6094 62, 6094 (2000).
67. A. S. Balankin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.5438 53, 5438 (1996).
68. O. Plischke, D. C. Vernon, B. Joós, and Z. Zhou, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.3129 60, 3129 (1999)
69. D. J. Jacobs, S. Dallakyan, G. G. Wood, and A. Heckathorne, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.061109 68, 061109 (2003).
70. X. Xing, S. Mukhopadhyay, and P. M. Goldbart, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.225701 93, 225701 (2004).
71. Unfortunately, the relative density of balls, which we were able to test in this work, varies over only one decade (0.047I Ï0 â0.502), and so, strictly speaking, a more correct statement is that the experimental data are consistent with the power-law scaling 10 with the universal scaling exponent.
72. We were not able to visualize a crumpling network in the black carbon paper of thickness 0.024 mm (see).
73. http://www.palisade.com
74. For the intermediate confinement ratios, the distribution of crumpling ridge lengths exhibits a crossover from a log-normal to a Î" distribution within a wide range K, as is suggested in.
75. F. H. Stillinger and T. A. Weber, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.25.978 25, 978 (1982)
76. S. Sastry, P. G. Debenedetti, and F. H. Stillinger, Nature (London) NATUAS 0028-0836 10.1038/31146 393, 554 (1998).
77. F. Sciortino, W. Kob, and P. Tartaglia, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.3214 83, 3214 (1999)
78. F. Sciortino and P. Tartaglia, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.107 86, 107 (2001).
79. H. M. Jaeger, S. R. Nagel, and R. P. Behringer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.68.1259 68, 1259 (1996).
80. S. F. Edwards and R. B. S. Oakeshott, Physica A PHYADX 0378-4371 10.1016/0378-4371(89)90034-4 157, 1080 (1989)
81. A. Mehta and S. F. Edwards, Physica A PHYADX 0378-4371 10.1016/0378-4371(89)90035-6 157, 1091 (1989).
82. A. Barrat, J. Kurchan, V. Loreto, and M. Sellitto, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.051301 63, 051301 (2001)
83. J. J. Brey and A. Prados, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.051302 68, 051302 (2003).
84. R. Blumenfeld and S. F. Edwards, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.114303 90, 114303 (2003).
85. R. Blumenfeld and S. F. Edwards, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.114303 90, 114303 (2003).
86. M. Pica Ciamarra, A. Coniglio, and M. Nicodemi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.158001 97, 158001 (2006).
87. The configurational temperature X enters as a parameter in the equilibrium distribution allowing us to substitute, as in the usual statistical mechanics, time averages, which are theoretically difficult to evaluate, by ensemble averages. In granular materials the dynamics from one stable microstate to another is induced by sequences of “taps,†in which the energy is pumped into the system in pulses. Due to inelastic collisions, the kinetic energy is totally dissipated after each tap and the system is again frozen in one of its inherent states. In the case of crumpling networks under uniaxial compression the role of taps plays the buckling of crumpling creases.