Nonlinear Transient Constitutive Theory With Multi-Fields Coupling Effects For GMM And Some Of Its Applications

As a new type of highly strategic smart materials in the21st century, giant magnetostrictive materials (GMM) have some distinct advantages such as large magnetostrictive strain, high electromechanical conversion efficiency, high energy density, fast response and so on. In such a case, GMM have been widely used in the modern new high-tech fields (e.g., transducers and magnetoelectric (ME) composites), and been highly concerned from academia and industry, especially for defense. However, many experiments have shown that GMM exhibit nonlinear characteristics of magnetic-elastic-thermal coupling and frequency-dependent hysteresis. Meanwhile, there is nonlinear coupling interaction between the constitutive behavior of GMM and the structural variation of device in GMM's actual applications. These two kinds of strongly nonlinear coupling interaction severely hinder the property characterization and optimization design as well as actual applications of smart devices whose key elements are GMM. Thus, a constitutive relationship study for GMM, and its application in the transducers and magnetoelectric composites are thoroughly investigated in this article.Firstly, based on the thermodynamic theory and the energy balance principle, a magnetic-elastic-thermal coupling magnetostriction model and a frequency-dependent magnetization model are established for GMM, respectively. Then the magnetostriction model and the magnetization model are coupled by effective magnetic field to constitute a nonlinear transient constitutive model with multi-fields coupling effects for GMM. The advantages of the magnetostriction model and the magnetization model are simultaneously inherited by the nonlinear transient constitutive model, and it can fully and effectively describe magnetic-elastic-thermal coupling behavior and frequency-dependent hysteretic behavior inherent to GMM observed in the experiments. Furthermore, it can effectively solve negative susceptibility issue at the reversal points of hysteresis loop. Thus, it provides the most perfect constitutive theory for the property characterization and further applications in the smart devices of GMM.Secondly, based on the nonlinear transient constitutive model established above, a nonlinear transient dynamic model with multi-fields coupling effects is proposed for giant magnetostrictive transducer system, in which strong coupling interaction between the nonlinear constitutive behavior of GMM and the structural dynamic behavior of the transducer system itself is accounted for through theorem of momentum. It is a fully coupled theoretical model, in which both the local coupling theory in material and global coupling theory in structure are incorporated. The numerical simulation results demonstrate the significance and necessity of simultaneously incorporating the local coupling theory and global coupling theory in the nonlinear transient dynamic model, and indicate that the nonlinear transient dynamic model established in this article can accurately and efficiently describe nonlinear magnetic-elastic-thermal coupling behavior and frequency-dependent hysteretic behavior for the giant magnetostrictive transducer system under magnetically unbiased and biased conditions. The above investigation provides the effective theory analysis method for the property characterization and optimization design as well as further applications in active vibration control of the giant magnetostrictive transducer.Finally, a novel nonlinear theoretical framework is proposed to investigate the coupled magnetic-elastic-electric effect involving linear and nonlinear coupling interactions for Terfenol-D based magnetoelectric laminated composites. Both the comparison between numerical simulation results and existing experimental data in quantity and the comparison between the nonlinear theoretical framework and linear theoretical framework in quality adequately demonstrate the accuracy and convenience of nonlinear theoretical framework established in this article, and indicate the significance and necessity of considering the nonlinear magnetic-elastic coupling characterization of Terfenol-D in the theoretical investigation. The above investigation provides the basic theoretical guidance for the property characterization and optimization design as well as further applications in actuator and sensor of the Terfenol-D based magnetoelectric laminated composites.After all, the work of this article preliminarily shows the broad perspective and potential advantage of the mechanical method in studying strongly nonlinear multi-fields coupling complex system, offsets the deficiency of theoretical investigation on GMM constitutive relationship, and provides theoretical basis for the property characterization and optimization design as well as actual application of the giant magnetostrictive transducers and Terfenol-D based magnetoelectric laminated composites.