A Multiscale Approach to Nonlinearity in Piezoelectric-Ferroelectric Smart Structures: From Micromechanics to Engineering

Abstract

A multiscale approach to the nonlinear electromechanical analysis of piezoelectric and ferroelectric structural elements is presented. The multiscale modeling ranges from the unit cell scale, in which the phenomena of domain switching originate, and goes through the grain scale, the material point scale, the continuum scale, and up to the structural element scale. A multiscale approach for the numerical solution of the governing equations of the nonlinear structural model is also presented. This approach accounts for the loading history dependency and the nonlinearity of the ferroelectric behavior by implementing an incremental iterative procedure and separate discretizations for the grain, the material point, and the structure scales. A numerical example of a ferroelectric beam under combined bending, compression, and electrical loading demonstrates the various multiscale aspects of the model and, particularly, the influence of the domain switching on the response at the different physical and mathematical scales. The findings of the article designate the multiscale approach as a meaningful step toward the implementation of ferroelectric materials in advanced smart structures with enhanced capabilities.