Crumpled wires in two dimensions

Abstract

Geometric and statistical properties of wires injected into a two-dimensional cavity with three different injection geometries are investigated. Complex patterns of folds are observed and studied as a function of the length of the wire. The mass-size relation and the distribution function n(s) of loops with internal area s formed as a consequence of the folded structure of the wire are examined. Several scaling laws are found and a hierarchical model is introduced to explain the experimental behavior observed in this two-dimensional crumpling process.

Condensation of elastic energy in two-dimensional packing of wires

“…The packing of a copper wire in our experiments is not perfectly reversible [3,4], however the degree of irreversibility is small, and considerable elastic energy remains stored in the cavity, as we confirm from the observation of the strong uncoiling of the wire when the cell is disconnected after a very long period. As we can see from Figure 1, the loops are units that have a bulge in one extremity, and in the other extremity the two branches of the loop merge.…”

“…On the other hand, from the power law scaling for M (R) shown in the upper inset of the figure we find D ′ S = 1.0 ± 0.1 in agreement with the box counting exponent D S . These exponents however, are markedly different from the mass exponent D = 1.9 ± 0.1, found for the entire mass distribution of wire within the cavity in the situation of maximum packing fraction [3,4]. These tests suggest that the support where energy is condensed, according to our previous definition, has a low dimension, which seems to be a well-defined property of the system.…”

“…A less studied problem in two-dimensional packing, which has great technological interest, is the search of a rigid system with a low packing fraction. An example of this last class of system is a single layer structure of loops obtained when a crushed wire is confined in a two-dimensional cavity [3]. This specific case yields rigid metallic structures with a maximum average occupation fraction of 14% of the area irrespective of the packing [4].…”

Plastic deformation of 2D crumpled wires

“…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].…”

“…Thus, considerable elastic energy remains stored in the cavity in different degrees after a long period if wires of these materials are used to generate the crumpled structures. The low dimensional packing of an elastic wire in a quasi-two-dimensional cavity of circular or square shape generates complex configurations of a cascade of loops with a fractal dimension D = 1.9 ± 0.1 as obtained from box-counting and mass-radius measurements [16]. Although the mass of wire in these heterogeneous packing structures distributes in an essentially two-dimensional support, from the practical point of view the maximum packing fraction observed within the cavity is significantly less than the unit.…”