Grain Orientation Scattering in Nonlinear Constitutive Modeling of Piezoelectric-ferroelectric Materials

Abstract

The ability to enhance and to improve the efficiency of micromechanical models for the coupled electromechanical constitutive behavior of piezoelectric materials in the nonlinear regime is investigated. Motivated by the limited strain actuation capabilities of the existing piezoelectric materials and structures, it is recognized that the nonlinear regime has to be explored. However, due to the complex, strongly coupled, and hysteretic behavior of the material, the quantitative prediction of its nonlinear response requires complex and time-consuming algorithms. In this study, the ability to improve the efficiency of the micromechanical algorithm by using a deterministic set of directions as a representative of the scattering of grain's orientation within the piezoelectric polycrystal is investigated. Various types of deterministic grain sets that include an equal area, a spiral, and Fekete grain sets are examined. The constitutive micromechanical model for the piezoelectric material and the algorithms for the generation of the various grain sets are presented and discussed. Numerical results that compare the capabilities of the model that uses the deterministic scattering approach and those that adopt a random scattering, which is commonly used today, are presented and discussed. Emphasis is placed on the ability to predict the complex nonlinear material response and on the computational efficiency. The article closes with a summary and conclusions.