Thermomechanical modeling and analysis of flexible structures with shape memory alloy actuators

A flexible active structure with shape memory alloys (SMA) usually involves structural and material nonlinearities, as well as strong coupling between the structure and shape memory alloys. Both residual deformation and hysteresis phenomena observed are crucial issues that influence the behavior and the ability to control an active structure. Furthermore, since there is a shift of the material parameters of SMA during cyclic thermomechanical loading in service, the task to provide a realistic model upon which to base a design becomes extremely difficult. It is those challenges which motivated the work of this dissertation.; This dissertation focuses on the modeling and analysis of active structures with shape memory alloys and attacks the associated phenomena mentioned above. In the first part of the dissertation, a thermomechanical model is developed to predict the structural response of a flexible beam with SMA wire actuators. A nonlinear static analysis is first carried out to investigate the deformed shape of a flexible cantilever beam caused by an externally attached SMA wire which is actuated electrically. The actuation force applied by the SMA actuator to the beam is evaluated by solving a coupled problem that combines the thermodynamic constitutive model of SMA and the heat conduction response of SMA with the structural model of the beam. The proposed model is used to simulate the experimental results, thus demonstrating the feasibility of using SMA actuators for shape control of active flexible structural systems. Modelling of the response of the elastomeric rods with an embedded actuator under the influence of gravitational force is also investigated with a general theory of flexible rods and an approximate formula. Both formulations allow to account for different temperature histories of actuation for shape memory alloy actuators.; In the next part of the dissertation, an identification method for the material parameters of SMA is presented with the application of an optimization theory. The method allows the determination of the material parameters for the SMA actuator which is being used on the active structures.; To incorporate the observed phenomena of the residual deformation during cooling of SMA, a modified thermodynamic constitutive model of SMA is derived based on previous work by Boyd and Lagoudas (1994). An internal variable of martensite volume fraction is decomposed into two parts: self-accommodated and detwinned martensite. The dissipation potentials, derived from the second law of thermodynamics, are explicitly given in 1-D for the evolution of the volume fractions of martensite. The concept of the critical stresses is introduced into the constitutive model. A prototype structure example is used to demonstrate the ability to predict the residual deformation and the recovery stress, which can be used as a guidance in design.; Finally, a phenomenological model and example for minor hysteresis loops of SMA is presented and extended to predict the hysteresis outputs with multiple thermodynamic driving forces. The efforts of this dissertation provides a framework to serve for the structural application of shape memory alloys.