Nonlinearity modeling of smart materials and structures

Hysteresis exists in many fields and receives much extensive study. It is one of the major challenges for the application and precise control of smart materials, such as shape memory alloys and piezoelectrical materials.;The modeling of hysteresis has been rate-independent for many years. The most popular approach is to use the classic Preisach model, which is a phenomenological model. The classic Preisach model divides the computation into two separate procedures based upon ascending or descending last inputs. This dissertation proposes a modified procedure for the computation. The modified procedure is explained geometrically. During the explanation, a general intrinsic physics is revealed for the classic Preisach model---the hysteresis is induced by the accumulation of the output residue. Finally, the proposed procedures are implemented numerically and verified experimentally.;In most practice, the input is not static or quasi-static and it has a rate as reported in much of the literature In this dissertation, different inputs are designed to test the influence of input rate on a piezoceramic stack actuator hysteresis experimentally. For the first time, this dissertation clearly shows that the dynamic hysteresis does not have the wiping-out and congruency properties, which are the sufficient and necessary conditions of the applicability of the classic Preisach model.;The stack actuator will relax after a nonzero rate input stops. The existing relaxation model is an exponential function derived from the classic Preisach model. Since this dissertation verified that the classic Preisach model does not apply for the stack actuator, an alternative model for the relaxation needs to be pursued. With experiments, this dissertation proposed a stretched exponential, or a complementary Weibull relaxation.;The relaxation will happen in the successively subsequent process. Such a relaxation process and the response of a fully relaxed input (has no impact from previous relaxation) comprise a rate-dependent response. The fully relaxed process was then investigated experimentally. The results indicate that the difference between the output of constant input rate and output of zero input rate is proportional to the input. Based on this discovery, a correction function is used to predict the fully relaxed process from the rate independent model.;Finally, the rate dependent hysteresis model for the stack actuator is proposed to be the superposition of the rate independent hysteresis, correction function and the relaxation from the previous monotonic input. This proposal is also one of the dissertation's contributions.;Piezoceramics actuated valveless micropump is a nonlinear smart structure. In this dissertation, an innovative numerical model consisting of electric-magnetic-fluid-structure coupling is built for it. The results agree very well with published experiments and the model provides a novel approach for the microfluidic device design and optimization.