A microscopically motivated constitutive model for piezoceramics under general electromechanical loading

Abstract

In the present paper a constitutive model for piezoceramics under multiaxial electromechanical loadings is developed for the engineering reliability analysis of piezoceramic components designed for so-called "smart" electromechanical sensor and actuator applications. At first a constitutive framework capable of representing general thermo-electromechnical processes is presented. This framework is established by using internal variables and is thermodynamically consistent with the Clasius-Duhem inequality for all admissible processes. Then, two scalar and two unit vector internal variables are introduced. One of the vectorial internal variables indicates the overall alignment direction of the c-axes of domains and the other variable represents the direction of the macroscopic irreversible polarization. The two scalar internal variables represent the fraction of domains whose c-axis is oriented in the alignment direction and the relative irreversible polarization, respectively. We indicate the microscopic foundation of the scalar internal variables in terms of an approximate orientation distribution function. A domain switching function is formulated in the driving force space to indicate the onset of the domain switching. The evolution equations of the internal variables are derived from the switching function by using the normality flow rule. Remanent strain and polarization are calculated as functions of the internal variables.In order to verify the underlying assumptions and to examine the ability of the model indescribing the material responses to electromechanical loadings, we demonstrate the simulation of various uniaxial and multiaxial loading processes.