Domain Switching Research Of PZT Piezoelectric Ceramics Based On Differential Evolution Optimization Algorithm

PZT piezoelectric ceramic is one of the most widely used and most typical piezoelectric ceramic.Because of its high electromechanical energy conversion efficiency,PZT piezoelectric ceramics are widely used in sensors and actuators in smart structures.The traditional piezoelectric constitutive equation can only show the linear response of the piezoelectric ceramics.With the increase of the applied field,the piezoelectric ceramics exhibit nonlinear ferroelectric response.The research and cognition of the nonlinear ferroelectric response of PZT piezoelectric ceramics are very limited,which restrict its further application.The main cause of nonlinearity is the change of the internal microstructure,that is,the domain change causes the nonlinear response of the material.The accurate description of the domain variable constitutive relation can be used to establish the relationship between the nonlinear response of the piezoelectric ceramic material and its microstructure.Therefore,it is very meaningful to study the nonlinear response behavior of piezoelectric materials.Although there are many methods of piezoelectric ceramic material nonlinear research,but mostly to fit the nonlinear response curve from the point of view of mathematics,has no actual physical meaning.The mechanism modeling is based on the internal structure of the material to study the nonlinearity.It can simulate the force,electricity and coupling nonlinear behavior effectively.In order to study the nonlinear response of the PZT ceramic material,the constitutive equation is modified from the constitutive equation of the material.It is considered that the domain change is a continuous process that occurs naturally in the process of minimizing the free energy of the grain.The finite element method and the transformation between local andglobal coordinate are used here to establish the relationship between the microscopic structure and the macroscopic response.By using the volume fraction of the domain as the optimization variable,the improved differential evolution algorithm is used to study the domain switching while the relation between volume fraction and crystal free energy.In this paper,the hysteresis loops and the butterfly curves of the rhombohedra phase and tetragonal phase PZT piezoelectric ceramics are studied and analyzed.The simulation results are in good agreement with the experimental data.