Modeling of hysteresis in deformation of rodlike objects toward their manipulation

Abstract

A systematic approach to the modeling of deformable rodlike objects is presented. Various rodlike objects such as cords and wires are manipulated in many manufacturing processes. In such processes, it is important for successful manipulation to evaluate their shapes on a computer in advance because their shapes can be changed easily and their deformation often shows hysteresis properties. In this paper, we develop an analytical method to model the shape of deformable rodlike objects including hysteresis properties. First, we investigate the mechanism of hysteresis. Second, the potential energy of a rodlike object and the geometric constraints imposed on it are formulated. The shape of the object can be derived by minimizing the potential energy under the geometric constraints. Thirdly, a procedure to compute the shape of a deformed rodlike object is developed by applying a non-linear programming technique. Finally, we show some numerical examples with hysteresis using our proposed method.