Entropic rigidity of a crumpling network in a randomly folded thin sheet

Abstract

We have studied experimentally and theoretically the response of randomly folded hyperelastic and elastoplastic sheets on the uniaxial compression loading and the statistical properties of crumpling networks. The results of these studies reveal that the mechanical behavior of randomly folded sheets in the one-dimensional stress state is governed by the shape dependence of the crumpling network entropy. Following up on the original ideas by Edwards for granular materials, we derive an explicit force-compression relationship which precisely fits the experimental data for randomly folded matter. Experimental data also indicate that the entropic rigidity modulus scales as the power of the mass density of the folded ball with universal scaling exponent.

34 page, 9 figures

References in corpus (25)

• Inherent Structure Entropy of Supercooled Liquids
• Crumpling a Thin Sheet
• The Statistical Mechanics of Membranes
• Boundary Layer Analysis of the Ridge Singularity in a Thin Plate
• The Geometry of Crumpled Paper
• Extension of the Fluctuation-Dissipation theorem to the physical aging of a model glass-forming liquid
• Edwards' measures: a thermodynamic construction for dense granular media and glasses
• Granular entropy: Explicit calculations for planar assemblies
• Stress condensation in crushed elastic manifolds
• Thermodynamics and Statistical Mechanics of dense granular media
• The Statistics of Crumpled Paper
• Anomalous strength of membranes with elastic ridges
• Network rigidity at finite temperature: Relationships between thermodynamic stability, the non-additivity of entropy and cooperativity in molecular systems
• Ridge Network in Crumpled Paper
• Scaling of the buckling transition of ridges in thin sheets
• Crescent Singularities in Crumpled Sheets
• Crumpling of a stiff tethered membrane
• Structural properties of crumpled cream layers
• Condensation of elastic energy in two-dimensional packing of wire
• Scaling of Entropic Shear Rigidity
• Power law scaling of lateral deformations with universal Poissons index for randomly folded thin sheets
• Folding and form: Insights from lattice simulations
• Closed model for granular compaction under weak tapping
• Phase transition of triangulated spherical surfaces with elastic skeletons
• Elasticity of Gaussian and nearly-Gaussian phantom networks

Cited by in corpus (9)

• The spontaneous emergence of ordered phases in crumpled sheets
• A model for the fragmentation kinetics of crumpled thin sheets
• Statistical distributions in the folding of elastic structures
• Topological crossovers in the forced folding of self-avoiding matter
• Layering in Crumpled Sheets
• Simulation of crumpled sheets via alternating quasistatic and dynamic representations
• Dynamics of Fluctuating Thin Sheets Under Random Forcing
• Thermally driven elastic membranes are quasi-linear across all scales
• The Structure of Fluctuating Thin Sheets Under Random Forcing