4 papers
Singularities, Structures and Scaling in Deformed Elastic m-Sheets
B. A. DiDonna, S. C. Venkataramani, T. A. Witten +1
The crumpling of a thin sheet can be understood as the condensation of elastic energy into a network of ridges which meet in vertices. Elastic energy condensation should occur in r…
Limitations on the smooth confinement of an unstretchable manifold
S. C. Venkataramani, T. A. Witten, E. M. Kramer +1
We prove that an m-dimensional unit ball D^m in the Euclidean space {\mathbb R}^m cannot be isometrically embedded into a higher-dimensional Euclidean ball B_r^d \subset {\mathbb R…
Stress condensation in crushed elastic manifolds
Eric M. Kramer, Thomas A. Witten
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 sta…
The von Karman equations, the stress function, and elastic ridges in high dimensions
Eric M. Kramer
The elastic energy functional of a thin elastic rod or sheet is generalized to the case of an M-dimensional manifold in N-dimensional space. We derive potentials for the stress fie…