Piezoelectric materials couple electrical and mechanical behaviour. They
are widely used as electronic filters, ultrasonic and acoustic
transducers, high voltage transformers, and so on. A recent and growing
application is in micro-actuators used in print heads and position
controllers. Whilst most of these applications are based on the linear
(small signal) material response, it is the non-linear (ferroelectric)
behaviour which is central to the manufacturing process, and to an
understanding of fatigue and crack propagation which limit component
performance. A central goal is a reliable constitutive model which
caters for the non-linear behaviour of ferroelectrics.
Three approaches to modelling are described:
an atomistic approach based on a simplified crystal unit cell;
a micromechanics approach based on crystal plasticity theory;
a phenomenological approach based on classical flow theory of plasticity.
The models are compared in terms of ability to capture material effects,
and practical usefulness. Some problems and current modelling issues are
raised.
