Nonlinear Constitutive Modeling of Piezoelectric Materials
Date
2013-01-29
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Abstract
The well-known piezoelectric constitutive equations are applicable to piezoceramics driven by low to moderate fields and therefore representing linear behavior. However, these materials are also known for their ferroelectric and ferroelastic nonlinearities particularly when input fields exceed coercive strength. Such nonlinearities are caused mainly by micro-structural changes in the material known as domain switching. Therefore, a constitutive model that can accommodate the domain switching process can help capture the nonlinear behavior of the material.
The past two decades have seen increasingly intensive activities in the attempt to build constitutive models to describe the piezoceramics nonlinearities. One of such models takes the advantage of existing linear constitutive equations. By decomposing the state variables into linear and internal components, the existing piezoelectric constitutive equations are augmented to include internal variables in describing the linear behavior while additional attention is devoted to dealing with the internal states pertinent to material's nonlinearities. The latter requires the modeling of the domain switching process. Together, the augmented linear constitutive equations and a domain switching model provide a complete nonlinear constitutive description. Although very successful in qualitatively capturing the polarization hysteresis and strain butterfly phenomena, a major shortcoming of this approach has been that it cannot match quantitatively with experimental data.
The objective of this research is to establish a constitutive model for piezoceramics that can not only qualitatively capture the material's nonlinear behavior over a large loading range, but also quantitatively match key characteristics from experimental data. In doing so, we have made three major contributions: 1) we discovered a flaw in the augmentation of linear constitutive equations for the use of materials in nonlinear regime and proposed a correct form of augmentation; 2) we proposed new domain switching rules based on the observations from single crystal experimental data; and 3) in the pursuit of model accuracy with quantitative description, we proposed the use of creep experiments to capture key characteristics related to time-dependent and rate-dependent responses. A finite element approach is taken to carry out numerical modeling at the microscopic level. Experimental data available in literature have been used to help with model development and validation.
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Applied Mechanics, Engineering--Mechanical
Citation
Zareian Jahromi, S. A. (2013). Nonlinear Constitutive Modeling of Piezoelectric Materials (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/27118