Stress condensation in crushed elastic manifolds

TL;DR

This paper investigates how elastic manifolds of dimensions 2 and 3 behave when compressed into small spheres within higher-dimensional spaces, revealing energy condensation into ridges under certain conditions.

Contribution

It provides analytical and simulation evidence that elastic energy condenses into ridges in specific dimensional regimes, extending understanding of manifold deformation under confinement.

Findings

Energy is uniformly distributed when N ≥ 2M.

Ridges form and dominate energy when N = M+1 and M > 1.

Ridges are straight over distances comparable to R.

Abstract

We discuss an M-dimensional phantom elastic manifold of linear size L crushed into a small sphere of radius R << L in N-dimensional space. We investigate the low elastic energy states of 2-sheets (M=2) and 3-sheets (M=3) using analytic methods and lattice simulations. When N \geq 2M the curvature energy is uniformly distributed in the sheet and the strain energy is negligible. But when N=M+1 and M>1, both energies appear to be condensed into a network of narrow M-1 dimensional ridges. The ridges appear straight over distances comparable to the confining radius R.