Our aim is the motivation of a macroscopic constitutive model for
engineering reliability analysis of piezoceramic components designed for
so-called ``smart'' electromechanical sensor and actuator applications.
Typically, such components are made of ferroelectric ceramics, mostly PZT
or modified PZT ceramics, which exhibit significant history-dependent
nonlinearities such as the well known dielectric, butterfly,
and ferroelastic hystereses due to domain switching processes.
Following an approach proposed previously by the authors
(Smart. Mater. Struct. 9(1999), 441 - 459),
we first propose a constitutive framework capable of representing
general thermo-electromechanical processes.
This framework makes use of internal variables and is thermodynamically
consistent with the Clausius-Duhem inequality for all admissible processes.
Next, we focus on uni-axial electromechanical loadings and introduce
microscopically motivated internal variables and their evolution equations.
In order to verify the underlying assumptions, we discuss the numerically
calculated model response to standard electromechanical loading paths.
This model is capable of reproducing the aforementioned typical hysteresys
phenomena and mechanical depolarization as well as other nonlinear
electromechanical coupling phenomena.
Furthermore, the model response exhibits rate-dependence, which
is typical in the response of ferroelectric ceramics.