On Λ-Elastica

In this paper, we investigate a transition from an elastica to a piece-wised elastica whose connected point defines the hinge angle phi(0) and we call the piece-wised elastica Lambda(phi 0)-elastica or Lambda-elastica. Such transition appears in the bending beam experiment when an elastic beam is gradually compressed and at some moment suddenly due to 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.