Crumpling of Curved Sheets: Generalizing Foeppl-von Karman

Details Crumpling of Curved Sheets: Generalizing Foeppl-von Karman Crumpling of Curved Sheets: Generalizing Foeppl-von Karman

2005-03-07

arxiv.org/abs/cond-mat/0503158v2

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

We generalize the F\"{o}ppl-von K\'arm\'an equations to an initially precurved sheet and present the underlying derivation. A geometrically computed moment of strain replaces the notion of bending moment and results in a geometric formulation of the theory of shells. As the curvature approaches zero, i.e., the sheet becomes flat, the new equations reduce to the classic F\"{o}ppl-von K\'arm\'an ones. The present theory solves the long-standing problem of formulating these equations for an a priori curved shell and applies, for instance, both to shell theory and to strongly curved biomembranes of cells as closed surfaces, exhibiting crumpling as the membrane thickness goes to zero.

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