Spontaneous Emergence of Ordered Phases in Crumpled Sheets

Abstract

X-ray tomography is performed to acquire 3D images of crumpled aluminum foils. We develop an algorithm to trace out the labyrinthian paths in the three perpendicular cross sections of the data matrices. The tangent-tangent correlation function along each path is found to decay exponentially with an effective persistence length that shortens as the crumpled ball becomes more compact. In the meantime, we observed ordered domains near the crust, similar to the lamellae phase mixed by the amorphous portion in lyotropic liquid crystals. The size and density of these domains grow with further compaction, and their orientation favors either perpendicular or parallel to the radial direction. Ordering is also identified near the core with an arbitrary orientation, exemplary of the spontaneous symmetry breaking.

Slow dynamics of stress and strain relaxation in randomly crumpled elasto-plastic sheets

“…Recently, there has been much interest in crumpling under the external loading of different kinds of thin materials, ranging from the microscopic level-graphene membranes to the macroscopic level-hand-folded paper and fault-related geological formations [1][2][3][4][5][6][7][8]. The relevant property that all thin materials share is that their stretching rigidity is much more than the bending rigidity.…”

Edwards's statistical mechanics of crumpling networks in crushed self-avoiding sheets with finite bending rigidity

“…[38] the increase of dp/dP was linked with the appearance of long-range correlations in the cluster structure of a crumpled sheet (see Ref. [26]). Based on this finding, the authors of Ref.…”

“…[22], In this context, it is pertinent to point out that the fractal dimensions of ball configuration and the fractal dimension of a set of balls folded by the same forces are generally different due to elastic strain relaxation after the confinement force is withdrawn [23]. It was also recognized that both fractal dimensions are independent of the sheet elastic properties [20][21][22][23][24][25][26][27][28][29][30], but may change due to plastic deformations of the sheet material [26,28,31]. Consequently, although the crumpling processes appear quite haphazard, the crumpling behavior is well defined in a statistical sense and rather well reproducible in experiments [13][14][15][16][17][18][19][20]32], Moreover, almost all thin materials display nearly the same scale invariant crumpling behavior [22], This has allowed the authors of Ref.…”

“…Another noteworthy feature of crumpling networks in randomly crushed thin sheets is their statistical scale invariance within a wide range of length scales [21,22], This gives rise to the fractal geometry of both a crumpled sheet configuration [22][23][24][25][26] and a set of balls folded from sheets of different sizes under the same confinement force [1,13,14,20,[27][28][29][30][31]. The relationships between the fractal dimensions of a crumpling network and sheet configuration were established in Ref.…”

Effect of ridge-ridge interactions in crumpled thin sheets

“…For instance, as the developable cones [3][4][5][6] increase in number and form the familiar network [7][8][9] of ridges and vertices, scientists still do not know how they collaborate to produce stunningly simple power laws between the crumpled ball size R and crumpling force F [10][11][12][13][14][15][16][17][18][19], R ∼ F −α and for the occurring frequency [20][21][22] of different noise intensities. One challenge is to understand how the crumpled sheet constructs spontaneously a highly porous and yet robust structure [23][24][25]. Proper theoretical tools are also in demand to tackle the complex many-body interactions among these deformations, especially the selfavoidance that plays an important role [14] at creating the glass-like interior after a series of highly non-equilibrium processes [26], similar to the random packing in a golf ball basket or salt jar.…”