Condensation of elastic energy in two-dimensional packing of wires

Abstract

Forced packing of a long metallic wire injected into a two-dimensional cavity leads to crushed structures involving a hierarchical cascade of loops with varying curvature radii. We study the distribution of elastic energy stored in such systems from experiments, and high-resolution digital techniques. It is found that the set where the elastic energy of curvature is concentrated has dimension DS = 1.0 ± 0.1, while the set where the mass is distributed, has dimension D = 1.9 ± 0.1.

Plastic deformation of 2D crumpled wires

“…The inset shows the corresponding box-counting plot [16,19]. Both figures are compatible with a fractal dimension D = 1.93 ± 0.12, as previously observed by using much less irreversible crushed structures made with wires of copper and steel, as well as with nylon fishing lines [16,19].…”

“…At this point, it is interesting to compare some basic and qualitatively new aspects of the irreversible 2D-CW exemplified in figure 1(b), with the more elastic and less irreversible structures of crumpled wires previously studied ( figure 1(a)) [16,17,19]. Firstly, the plastic structures are more heterogeneous and a scaling cascade of loops is much less evident.…”

“…At this stage the circular cell is maintained in the horizontal position. The interested reader is referred to previous works [16,17,19] for further details on how to obtain the nearly circular 2D-CW. After the jammed stage to be reached, the 2D-CW configurations are transferred to the rectangular cell which is disposed vertically in the press frame as indicated in figure 2(a).…”

“…In fact, it is close to 0.15 (i.e. much smaller than typical packing fractions of 0.82 − 0.84 obtained with the random close packing of discs), irrespective the material of the wire, the angle formed between the injection channels, and other details [16,17,19].…”

“…Only recently rigid, non-compact, heterogeneous crumpled structures of wires of circular shape were obtained in two dimensions (shortly, 2D-CW) from packing processes of a single layer of wire injected trough channels into a quasi-two-dimensional cavity [16][17][18][19][20][21][22]. In particular, in the first studies of 2D crumpled structures were used wires of copper or steel and nylon fishing lines [16,17,19], which give origin to quasi-reversible or almost perfectly reversible packing structures of loops of the type illustrated in figure 1(a). The degree of reversibility mentioned here can be evaluated for instance, from the level of recovery or uncoiling of the wire when the confining wall of the cavity is withdrawn.…”