Multi-Scale Modeling for Electro-Mechanical Coupling of Ferroelectrics

摘要

A multi-scale modeling scheme of electro-mechanical coupling of ferroelectric materials is proposed.The scheme is effective for quantitatively analyzing relationships among variables of micro/meso/macroscopic and structural scales.The methodology is exemplified through investigating behavior of PLZT.The key for connection of variables at different scales is through the remanant polarization and remanant strain at the meso-cell.The remanant variables,on one hand,are connected through volume average to those at the macroscopic scale.On the other hand,remanant variables are quantitatively connected to microstructure status at the microscopic scale.A much simple formulation for describing the complicated nonlinear dissipative process of domain switching is proposed which can account for the evolution of microstructures.This is physically sound in the sense that it can describe progressive domain switching with the prediction capability of switching saturation and limited interactions between different switching systems.Numerical results show that the well-known nonlinear butterfly curve of strain versus electrical field is described,and the predicted effects of compressive stress are consistent with the existing experimental results.