Simulations Of Statistical Domain Switching Model Of 8/65/35 PLZT Based On Self-adaptive Differential Evolution Algorithm

Piezoelectric ceramic has been widely used in aspects like sensing conversion materials and driving devices in intelligent systems because of its piezoelectric effect under applied electric field or force field.Researchers think piezoelectric effect is linear and reversible in traditional theories,however,experimental research and practical application has shown that macroscopic response of piezoelectric ceramic is nonlinear under strong electric field or force field.Learning and establishing the nonlinear constitutive model for piezoelectric ceramic is of important theoretical guiding significance to predict the nonlinear response and application of piezoelectric ceramic.In order to build a proper constitutive model of piezoelectric ceramic,this design first introduced a circular random distribution to simulate the random distribution of the simplified two-dimensional electric domain model.The relation between the spontaneous polarization and spontaneous strain of single cell and residual polarization and residual strain of the whole material is inferred by defining electric domain concentration parameter ? combining with coordinate system transformation(the transition between micro parameters and macro Variables).Because the model is very sensitive to the spontaneous polarization and spontaneous strain of a single cell,so global optimization is needed for the two parameters.Self-adaptive differential evolution algorithm is chosen as the optimization algorithm of the paper for its quick convergence and simple to use.The control parameters of the algorithm can be self-adaptive,which helps saving time of parameter adjustment and improving the effect of global optimization.According to different applied fields the theoretical simulation can divided into two parts,electric field and force field.In order to verify the correctness of model and precision of optimization,the constitutive model of material parameters such as piezoelectric coefficient and dielectric coefficient are supposed to be unknown and solved by reverse solution of the model.Lead lanthanum zironate titanate(8/65/35 PLZT)is chose as the researching material due to its industrial application and excellent material performance.Optimization results are compared with typical macroscopic response of materials such as hysteresis loop(electric field),butterfly loop(electric field),stress versus strain(force field)and stress versus electric displacement(force field),the values of inverse problem parameter are compared with literature values.The algorithm converges quickly and a good agreement is achieved between retrieved values and experiment results,which proves the precision of the optimization process and the correctness of model.The paper presents the use of intelligent algorithm to improve the performance of material constitutive model,which has a certain reference value of research and application for the research of nonlinear constitutive model of piezoelectric ceramic.