Statistical distributions in the folding of elastic structures

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that leads to complex fold patterns. By studying, both experimentally and numerically, the case of a rod confined isotropically into a disc, we show that the emergence of the complexity is associated with a well-defined underlying statistical measure that determines the energy distribution of sub-elements, 'branches', of the rod. This result suggests that branches act as the 'microscopic' degrees of freedom laying the foundations for a statistical mechanical theory of this athermal and amorphous system.

[1]  Y. C. Lin,et al.  Crumpling under an ambient pressure. , 2008, Physical review letters.

[2]  Thin elastic plates: On the core of developable cones , 2002 .

[3]  Intrinsically anomalous self-similarity of randomly folded matter. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Pablo G. Debenedetti,et al.  Supercooled liquids and the glass transition , 2001, Nature.

[5]  Julian F. V. Vincent,et al.  The geometry of unfolding tree leaves , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[6]  M. Mézard,et al.  Out of equilibrium dynamics in spin-glasses and other glassy systems , 1997, cond-mat/9702070.

[7]  H. Herrmann,et al.  Morphological phases of crumpled wire. , 2008, Physical review letters.

[8]  B. Didonna,et al.  Scaling of the buckling transition of ridges in thin sheets. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  G. Gompper,et al.  Forced crumpling of self-avoiding elastic sheets , 2006, Nature materials.

[10]  D. Morse,et al.  Scaling Properties of Stretching Ridges in a Crumpled Elastic Sheet , 1995, Science.

[11]  Andrea J. Liu,et al.  Effective temperatures of a driven system near jamming. , 2001, Physical review letters.

[12]  Stress Condensation in Crushed Elastic Manifolds , 1996, cond-mat/9609037.

[13]  S. Chaieb,et al.  Experimental Study of Developable Cones , 1998 .

[14]  D. Blair,et al.  Geometry of crumpled paper. , 2004, Physical review letters.

[15]  M. Trejo,et al.  Spiral patterns in the packing of flexible structures. , 2006, Physical review letters.

[16]  Andrea J. Liu,et al.  Nonlinear dynamics: Jamming is not just cool any more , 1998, Nature.

[17]  A. Boudaoud,et al.  Energy distributions and effective temperatures in the packing of elastic sheets , 2008, 0804.3149.

[18]  Y. Hwu,et al.  X-ray tomography of a crumpled plastoelastic thin sheet. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Crumpling a thin sheet. , 2001, Physical review letters.

[20]  J. Kurchan,et al.  Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment , 2002, Nature.

[21]  Intrinsically anomalous roughness of randomly crumpled thin sheets. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  S. Douady,et al.  A Global Regulation Inducing the Shape of Growing Folded Leaves , 2009, PloS one.

[23]  Condensation of elastic energy in two-dimensional packing of wires. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Y. Hwu,et al.  Spontaneous emergence of ordered phases in crumpled sheets. , 2009, Physical review letters.

[25]  R. E. de Souza,et al.  Scaling properties in the packing of crumpled wires. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Rob Phillips,et al.  Forces during bacteriophage DNA packaging and ejection. , 2004, Biophysical journal.

[27]  A. Balankin,et al.  Entropic rigidity of a crumpling network in a randomly folded thin sheet. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Exactly solvable model for driven dissipative systems. , 2004, Physical review letters.

[29]  Definition and relevance of nonequilibrium intensive thermodynamic parameters. , 2005, Physical review letters.

[30]  Crescent singularities in crumpled sheets. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Structural properties of crumpled cream layers , 2007, 0705.2218.

[32]  T. Witten.  Stress focusing in elastic sheets , 2007 .

[33]  E. Katzav,et al.  A statistical approach to close packing of elastic rods and to DNA packaging in viral capsids , 2006, Proceedings of the National Academy of Sciences.

[34]  Boundary layer analysis of the ridge singularity in a thin plate. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  J. Timonen,et al.  The effect of plasticity in crumpling of thin sheets. , 2009, Nature materials.

[36]  A. Hansen,et al.  Ridge network in crumpled paper. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Asymptotic Shape of a Fullerene Ball , 1993 .

[38]  L. Mahadevan,et al.  Conical dislocations in crumpling , 1999, Nature.

[39]  S. Edwards,et al.  Theory of powders , 1989 .

[40]  Y. Couder,et al.  Dynamics of singularities in a constrained elastic plate , 2000, Nature.

[41]  T. Aste,et al.  An invariant distribution in static granular media , 2006, cond-mat/0612063.

[42]  Y. C. Lin,et al.  Crumpling wires in two dimensions. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  ENERGY FLOW, PARTIAL EQUILIBRATION, AND EFFECTIVE TEMPERATURES IN SYSTEMS WITH SLOW DYNAMICS , 1997, cond-mat/9611044.

[44]  F. Gallet,et al.  Buckling in a solid Langmuir monolayer: light scattering measurements and elastic model , 1998 .

[45]  M. Gomes,et al.  The crumpled state of some non-equilibrium fractal surfaces , 1990 .

[46]  E. Katzav,et al.  Folding of flexible rods confined in 2D space , 2007 .

[47]  Colson,et al.  Buckling of polymerized monomolecular films. , 1994, Physical review letters.

[48]  L. Mahadevan,et al.  Conical Surfaces and Crescent Singularities in Crumpled Sheets , 1998 .

[49]  S. Roux,et al.  Experimental study of the roughness of crumpled surfaces , 1996 .

[50]  A. Boudaoud,et al.  Statistics of crumpled paper. , 2005, Physical review letters.

[51]  A. Balankin,et al.  Scaling properties of randomly folded plastic sheets. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  Y. Pomeau,et al.  Crumpled paper , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[53]  H. Hentschel,et al.  Effective temperature in elastoplasticity of amorphous solids , 2009, 0908.4090.

[54]  J. Brackenbury,et al.  Wing folding and free‐flight kinematics in Coleoptera (Insecta): a comparative study , 1994 .

[55]  H. Jaeger,et al.  Granular solids, liquids, and gases , 1996 .

[56]  Loreto,et al.  Edwards' measures for powders and glasses , 2000, Physical review letters.

[57]  T. Witten,et al.  Properties of ridges in elastic membranes , 1996, cond-mat/9609068.