Crumpling of Curved Sheets: Generalizing Foeppl-von Karman
  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. 
J. Leo van Hemmen, Mark A. Peterson