A Percolation Based Micromechnical Constitutive Model for Flexible Piezoelectric Paint

A percolation theory based micromechanics model is proposed in this paper to describe the elastoelectric properties of flexible piezoelectric paint. Piezoelectric paint consists of tiny piezoelectric ceramic particles randomly dispersed in a polymer matrix and therefore belongs to the “0–3” piezoelectric composite. Because of its ease of application, piezoelectric paint can be readily fabricated into sensing element with complex patterns. To guide the sensor design, a micromechanics model for describing the electromechanical properties of piezoelectric paint is proposed. The focus of this research is given to piezoelectric paint with a piezoelectric ceramic volume fraction ranging from 35% to 65%, for which some of the active particles form 1–3 connectivity, leading to higher piezoelectric activity than previous models for piezoelectric 0–3 composites predict. Percolation theory is used to model the quick increase of piezoelectric activity after a threshold level of piezoelectric ceramic particle volume fraction is exceeded in the piezoelectric paint. The effect of piezoelectric ceramic volume fraction on the electromechanical properties of piezoelectric paint is first examined. The proposed model for piezoelectric paint considers the effect of air void contents and poling field on the elastoelectric properties of piezoelectric paint. The parameters of the present model are calibrated with experimental data.