The physics of tightly packed structures of a wire and other threadlike materials confined in cavities has been explored in recent years in connection with crumpled systems and a number of topics ranging from applications to DNA packing in viral capsids and surgical interventions with catheter to analogies with the electron gas at finite temperature and with theories of two-dimensional quantum gravity. When a long piece of wire is injected into two-dimensional cavities, it bends and originates in the jammed limit a series of closed structures that we call loops. In this work we study the extraction of a crumpled tightly packed wire from a circular cavity aiming to remove loops individually. The size of each removed loop, the maximum value of the force needed to unpack each loop, and the total length of the extracted wire were measured and related to an exponential growth and a mean field model consistent with the literature of crumpled wires. Scaling laws for this process are reported and the relationship between the processes of packing and unpacking of wire is commented upon.

Abstract. The present work deals with the injection and packing of a flexible polymeric rod of length L into a simply connected rectangular domain of area XY . As the injection proceeds, the rod bends over itself and it stores elastic energy in closed loops. In a typical experiment N of these loops can be identified inside the cavity in the jammed state. We have performed an extensive experimental analysis of the total length L(N, X, Y ) in the tight packing limit, and have obtained robust power laws relating these variables. Additionally, we have examined a version of this packing problem when the simply connected domain is partially occupied with free discs of fixed size. The experimental results were obtained with 27 types of cavities and obey a single equation of state valid for the tight packing of rods in domains of different topologies. Besides its intrinsic theoretical interest and generality, the problem examined here could be of interest in a number of studies including package models of DNA and polymers in several complex environments.

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The continuous packing of a flexible rod in two-dimensional cavities yields a countable set of interacting domains that resembles nonequilibrium cellular systems and belongs to a new class of lightweight material. However, the link between the length of the rod and the number of domains requires investigation, especially in the case of non-simply connected cavities, where the number of avoided regions emulates an effective topological temperature. In the present article we report the results of an experiment of injection of a single flexible rod into annular cavities in order to find the total length needed to insert a given number of loops (domains of one vertex). Using an exponential model to describe the experimental data we quite minutely analyze the initial conditions, the intermediary behavior, and the tight packing limit. This method allows the observation of a new fluctuation phenomenon associated with instabilities in the dynamic evolution of the packing process. Furthermore, the fractal dimension of the global pattern enters the discussion under a novel point of view. A comparison with the classical problems of the random close packing of disks and jammed disk packings is made.

The injection of a long flexible rod into a two-dimensional domain yields a complex pattern commonly studied through the elasticity theory, packing analysis, and fractal geometries. ‘Loop’ is a one-vertex entity that naturally formed in this system. The role of the elastic features of each loop in 2D packing has not yet been discussed. In this work, we point out how the shape of a given loop in the complex structure allows estimating local deformations and forces. First, we build sets of symmetric free loops and perform compression experiments. Then, tight packing configurations are analyzed using image processing. We find that the dimensions of the loops, confined or not, obey the same dependence on the deformation. The results are consistent with a simple model based on 2D elastic theory for filaments, where the rod adopts the shape of Euler’s elasticas between its contact points. The force and the stored energy are obtained from numerical integration of the analytic expressions. In an additional experiment, we obtain that the compression force for deformed loops corroborates the theoretical findings. The importance of the shape of the loop is discussed and we hope that the theoretical curves may allow statistical considerations in future investigations.