Study On Theoretical Modeling Of Interfacial Effects Within Piezoelectric Composites And Its Numerical Implementation Via XFEM

In recent years, for the rapid development of smart materials, piezoelectric material has become a hot research focus due to its electromechanical coupling property. However, practical applications of pure piezoelectric materials are constrained with their inherent brittle which could result in the cracks and stress concentration under the elastic load and electric load. In order to improve the overall strength property and value of applications of piezoelectric material, researchers embed the piezoelectric material into the polymer matrix. Hence, piezoelectric composites have kept the electromechanical coupling property and improved its hardness at the same time. It has been applied in medical, acoustics, military and so forth. In practical fabrication of piezoelectric fiber composites, thin transition layers with distinct material property often emerge between the fiber phase and the matrix phase due to their chemical reaction. Generally speaking, the microstructure and physical property of the transition layers are quite different from the fiber phase and the matrix phase. It has great impact on the macroscopic electromechanical coupling properties of piezoelectric composites. Therefore, it is rather significant to establish a theoretical model and develop an efficient numerical implementation to deal with the effect of the interface on the macro properties of the piezoelectric composites. As for the interface of piezoelectric composites, the research often establishes under the consumption of two phase materials perfect interface. That is to say, the displacement, potential, traction and normal electric displacement are continuous across the interface. In fact, micro defects like voids and holes in the interphase could result in the jumps of physical fields across the interphase, that is to say, such interface is imperfect. Ever since the1980s, the discontinuous issues of imperfect interface have attracted many researchers. There have been three models of imperfect interface already, which are membrane-type imperfect interface, spring-layer imperfect interface, and general imperfect interface. Among all, spring-layer imperfect interface model is the most feasible and simplest one which has been widely used. As for this interface model, the displacement vector and the electric potential suffer jumps across an interface, while both the traction and the normal electric displacement are continuous across the same interface and proportional to the displacement vector and the electric potential jumps where the coupled material parameters interne. According to the literature research, the current studies on properties of piezoelectric materials are focusing on the hypothesis of perfect interface, which neglects the jump relations of the physical fields across the interface; as for numerical implementation, most of the modeling and simulations are basing on the classical finite element method. Nevertheless, there are few reports on the he numerical implementation of imperfect interfacial problems in piezoelectric composites within XFEM.The present thesis aims to illuminate an efficient numerical approach to cope with the interface effects depicted by the piezoelectric spring type interface model. I launched out the following contents:(1) According to the general imperfect interface model developed by Gu and He for coupled multi-field phenomena, a compact expression of the jump relations across the general imperfect interface within fiber-reinforced piezoelectric composites is deduced. Furthermore, it is reduced to the spring type interface model. It laid a foundation for the further analysis upon interface effect.(2) Basing on the jump relations of the imperfect interface model, the governing piezoelectric equations are specified covering the spring type imperfect interface. The weak form is deduced by the virtual work theorem. Within the framework of XFEM and LSM, the discrete equilibrium equations are deduced. It offers theoretical support for the subsequent numerical approaches.(3) Set a benchmark problem within the single cylindrical fiber, the analytic solution of the model is deduced. It sets criteria for the following work. Meanwhile, I compile the program of XFEM and develop the numerical validation on benchmark problems. The convergence analysis is then carried out for validation of the elaborated numerical procedure. And basing on the elaborated numerical approach and the benchmark problem, the correctness and versatility are validated.