Numerical simulation of shape memory actuators in mechatronics

Abstract

This paper deals with shape memory alloys (SMA) as temperature controlled actuators in mechatronic applications. The mathematical model consists of a coupled system of partial differential and differential-algebraic equations where continuum equations describe the evolution of deformation and temperature while rigid body equations and control laws define the interaction with the mechatronic device. Both modeling and numerical issues will be addressed. In particular, by applying the method of lines with finite elements, the overall problem is reduced to a differential-algebraic system in time that is shown to be of index two. Simulation results for a robotics application illustrate the approach. © 2008 Springer-Verlag Berlin Heidelberg.