The compressive strength of crumpled matter

Abstract

Crumpling a sheet creates a unique, stiff and lightweight structure. Use of crumples in engineering design is limited because there are not simple, physically motivated structure-property relations available for crumpled materials; one cannot trust a crumple. On the contrary, we demonstrate that an empirical model reliably predicts the reaction of a crumpled sheet to a compressive force. Experiments show that the prediction is quantitative over 50 orders of magnitude in force, for purely elastic and highly plastic polymer films. Our data does not match recent theoretical predictions based on the dominance of building-block structures (bends, folds, d-cones, and ridges). However, by directly measuring substructures, we show clearly that the bending in the stretching ridge is responsible for the strength of both elastic and plastic crumples. Our simple, predictive model may open the door to the engineering use of a vast range of materials in this state of crumpled matter.

Understanding the Role of Self-Adhesion in Crumpling Behaviors of Sheet Macromolecules

“…It is observed that the evolutionary trend of ΔPE total remains roughly the same during the crumpling process regardless of values of D 0 (Figure a) and k θ (Figure b), which implies that the in-plane stiffness plays a relatively minor role in their crumpling behavior. This is generally in line with the previous study showing that the formed ridges associated with in-plane stiffness are the minimal crumples in terms of energy storage compared to other crumples (i.e., bend, fold, and d-cones) . This is characteristically different from the evolution of ΔPE total for different k ϕ (Figure c) and ε LJ (Figure d)the well depth of ΔPE total becomes greater for smaller k ϕ (i.e., more flexible) or larger ε LJ (i.e., more adhesive).…”

“…This is generally in line with the previous study showing that the formed ridges associated with in-plane stiffness are the minimal crumples in terms of energy storage compared to other crumples (i.e., bend, fold, and d-cones). 61 This is characteristically different from the evolution of ΔPE total for different k ϕ (Figure 2c) and ε LJ (Figure 2d) the well depth of ΔPE total becomes greater for smaller k ϕ (i.e., more flexible) or larger ε LJ (i.e., more adhesive). Note that the system reaches a quasi-equilibrium state when ΔPE total reaches a local minimum value.…”

Roughness tolerant pressure sensitive adhesives made of sticky crumpled sheets

“…30,34,36,38 A recent practical advance has been the establishment of a simple, empirical, scaling rule for describing the compressive load held by a crumpled ball. 34,35,37 If a crumpled ball is compressed between two parallel plates, the force, F cm is related to the plate separation H as: F cm = Ēt 2 (2 R / H ) α ,where Ē is the plane strain modulus of the sheet, t is its thickness, R the radius of the crumpled ball and α is an exponent. Experimentally, the exponent is known to vary from material to material, but does seem to have well defined average values.…”

Transition to stress focusing for locally curved sheets

“…A U-shaped scar is found at the tip of a d cone and its formation is the consequence of the sheet avoiding diverging curvatures at the apex. This picture of stress focusing can be generalized to crumpling [7][8][9][10][11][12]: A crumpled configuration is a state occupying a small volume that combines regions approaching developability and localized ridges focusing the stretching deformations.…”