Elastica theory

The elastica theory is a theory of mechanics of solid materials developed by Leonhard Euler that allows for very large scale elastic deflections of structures.

Euler (1744) and Jakob Bernoulli developed the theory for elastic lines (yielding the solution known as the elastica curve) and studied buckling.

Later elastica theory was generalized together by the Cosserat brothers François and Eugene into a geometric theory with intrinsic directions at each point (1907).

For most boundary conditions several solutions exist simultaneously.

A modern treatise of the planar elastica with full account of bifurcation and instability has been recently presented by Bigoni.