Effect of ridge-ridge interactions in crumpled thin sheets

Fold analysis of crumpled sheets using microcomputed tomography

Hand-crumpled paper balls involve intricate structure with a network of creases and vertices, yet show simple scaling properties, which suggests self-similarity of the structure. We investigate the internal structure of crumpled papers by the microcomputed tomography (micro-CT) without destroying or unfolding them. From the reconstructed three-dimensional (3D) data, we examine several power laws for the crumpled square sheets of paper of the sizes L=50-300 mm and obtain the mass fractal dimension D_{M}=2.7±0.1 by the relation between the mass and the radius of gyration of the balls and the fractal dimension 2.5≲d_{f}≲2.8 for the internal structure of each crumpled paper ball by the box counting method in the real space and the structure factors in the Fourier space. The data for the paper sheets are consistent with D_{M}=d_{f}, suggesting that the self-similarity in the structure of each crumpled ball gives rise to the similarity among the balls with different sizes. We also examine the cellophane sheets and the aluminium foils of the size L=200 mm and obtain 2.6≲d_{f}≲2.8 for both of them. The micro-CT also allows us to reconstruct 3D structure of a line drawn on the crumpled sheets of paper. The Hurst exponent for the root-mean-square displacement along the line is estimated as H≈0.9 for the length scale shorter than the scale of the radius of gyration, beyond which the line structure becomes more random with H∼0.5.

Crumpling an elastoplastic thin sphere

The phenomenon of crumpling is common in nature and our daily life. However, most of its properties, such as the power-law relation for pressure versus density and the ratio of bending and stretching energies, as well as the interesting statistical properties, were obtained by using flat sheets. This is in contrast to the fact that the majority of crumpled objects in the real world are three-dimensional. Notable examples are car wreckage, crushed aluminum cans, and blood cells that move through tissues constantly. In this work, we did a thorough examination of the properties of a crumpled spherical shell, hemisphere, cube, and cylinder via experiments and molecular-dynamics simulations. Physical arguments are provided to understand the discrepancies with those for flat sheets. The root of this disparity is found to lie less in the nonzero curvature, sharp edges and corner, and open boundary than in the dimensionality of the sample.

Crumpling-origami transition for twisting cylindrical shells

Origami and crumpling are two processes to reduce the size of a membrane. In the shrink-expand process, the crease pattern of the former is ordered and protected by its topological mechanism, while that of the latter is disordered and generated randomly. We observe a morphological transition between origami and crumpling states in a twisted cylindrical shell. By studying the regularity of the crease pattern, acoustic emission, and energetics from experiments and simulations, we develop a model to explain this transition from frustration of geometry that causes breaking of rotational symmetry. In contrast to solving von Kármán-Donnell equations numerically, our model allows derivations of analytic formulas that successfully describe the origami state. When generalized to truncated cones and polygonal cylinders, we explain why multiple and/or reversed crumpling-origami transitions can occur.

Tailoring relaxation dynamics and mechanical memory of crumpled materials by friction and ductility

Crumpled sheets show slow mechanical relaxation and long lasting memory of previous mechanical states. By using uniaxial compression tests, the role of friction and ductility on the stress relaxation dynamics of crumpled systems is investigated. We find a material dependent relaxation constant that can be tuned by changing ductility and adhesive properties of the sheet. After a two-step compression protocol, nonmonotonic aging is reported for polymeric, elastomeric and metal sheets, with relaxation dynamics that are dependent on the material's properties. These findings can contribute to tailoring and programming of crumpled materials to get desirable mechanical properties.

Effect of the material properties on the crumpling of a thin sheet

While simple at first glance, the dense packing of sheets is a complex phenomenon that depends on material parameters and the packing protocol. We study the effect of plasticity on the crumpling of sheets of different materials by performing isotropic compaction experiments on sheets of different sizes and elasto-plastic properties. First, we quantify the material properties using a dimensionless foldability index. Then, the compaction force required to crumple a sheet into a ball as well as the average number of layers inside the ball are measured. For each material, both quantities exhibit a power-law dependence on the diameter of the crumpled ball. We experimentally establish the power-law exponents and find that both depend nonlinearly on the foldability index. However the exponents that characterize the mechanical response and morphology of the crumpled materials are related linearly. A simple scaling argument explains this in terms of the buckling of the sheets, and recovers the relation between the crumpling force and the morphology of the crumpled structure. Our results suggest a new approach to tailor the mechanical response of the crumpled objects by carefully selecting their material properties.

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

This paper is devoted to the crumpling of thin matter. The Edwards-like statistical mechanics of crumpling networks in a crushed self-avoiding sheet with finite bending rigidity is developed. The statistical distribution of crease lengths is derived. The relationship between sheet packing density and hydrostatic pressure is established. The entropic contribution to the crumpling network rigidity is outlined. The effects of plastic deformations and sheet self-contacts on crumpling mechanics are discussed. Theoretical predictions are in good agreement with available experimental data and results of numerical simulations. Thus, the findings of this work provide further insight into the physics of crumpling and mechanical properties of crumpled soft matter.