  In this paper, we investigate a transition from an elastica to a piece-wised
elastica whose connected point defines the hinge angle $\phi_0$; we refer the
piece-wised elastica $\Lambda_{\phi_0}$-elastica or $\Lambda$-elastica. The
transition appears in the bending beam experiment; we compress elastic beams
gradually and then suddenly due the rupture, the shapes of $\Lambda$-elastica
appear. We construct a mathematical theory to describe the phenomena and
represent the $\Lambda$-elastica in terms of the elliptic $\zeta$-function
completely. Using the mathematical theory, we discuss the experimental results
from an energetic viewpoint and numerically show the explicit shape of
$\Lambda$-elastica. It means that this paper provides a novel investigation on
elastica theory with rupture.

Classical Physics;Differential Geometry