The von Karman equations, the stress function, and elastic ridges in high dimensions

Details The von Karman equations, the stress function, and elastic ridges in high dimensions The von Karman equations, the stress function, and elastic ridges in high dimensions

1996-08-09

arxiv.org/abs/cond-mat/9608050v2

Physics

Condensed Matter

corrected references, 27 pages, RevTeX + epsf, 2 figures, Submitted to J. Math. Phys

Scientific paper

10.1063/1.531893

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 field and curvatures and find the generalized von Karman equations for a manifold in elastic equilibrium. We perform a scaling analysis of an M-1 dimensional ridge in an M = N-1 dimensional manifold. A ridge of linear size X in a manifold with thickness h << X has a width w ~ h^{1/3}X^{2/3} and a total energy E ~ h^{M} (X/h)^{M-5/3}. We also prove that the total bending energy of the ridge is exactly five times the total stretching energy. These results match those of A. Lobkovsky [Phys. Rev. E 53, 3750 (1996)] for the case of a bent plate in three dimensions.

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