these lines there is growing interest in the design and control of smart structures systems with embedded sensors and actuators that provide enhanced ability to program a desired response from a system. The ability to sense real time conditions, i.e., the factors that contribute to turbulence and therefore resistance in a given environment, would be welcome and useful. Applications of interest include: (a) smart helicopter rotors with actuated flaps that alter the aerodynamic and vibrational properties of the rotor in conjunction with evolving flight conditions and aerodynamic loads; and (b) smart fixed wings with actuators that alter airfoil shape to accommodate changing drag/lift conditions. In these and other examples, key technologies include actuators based on materials that respond to changing electric, magnetic, and thermal fields via piezoelectric, magnetostrictive and thermo elasto plastic
Typically such materials exhibit complex nonlinear and hysteretic responses. Controlling such materials is thus a challenge. The present work is concerned with the development of a hyteretics based model for magnetostrictive material that captures hysteretic phenomena.
Materials science is constantly discovering new avenues of research. The idea of materials that are reactive and can respond to external stimuli is not new. Materials with "shape memory" are well known (Proceedings of Shape Memory and Superelastic Technologies, 1997, pp 636). Materials that can be controlled and altered in critical situations, are of more recent vintage.
Active materials used as actuators in engineering applications exhibit nonlinear hysteretic response. The control of deformations of active structures, especially under cyclic loading, is therefore a challenging problem. Currently, there are physically motivated constitutive models of active materials
and empirical models based on identification procedures. The first group of models includes mi...