Finite element analysis of a multilayer piezoelectric actuator taking into account the ferroelectric and ferroelastic behaviors

Abstract

Ferroelasticity and ferroelectricity are the non linear behaviours exhibited by piezoceramics, especially in the case of high electric field or stress. Many studies have focused on the role of ferroelastic and ferroelectric switching in fracture of actuators. However, engineering reliability analyses are carried out with tools like finite element software that do not take into account these non linear phenomena. To overcome such a problem, a simplified phenomenological constitutive law has been developed and describe the hysteresis effect of piezoceramics. It is time-independent and relies on the introduction of remnant polarization and remnant strain as internal variables. Two loading surfaces, similar to the ones used in plasticity, provide the evolution laws for the internal variables. Besides, polarization-induced anisotropy in the piezoelectric tensor is taken into account. That constitutive law has been implemented in the commercial software ABAQUS. It has been necessary to develop a finite element with electrical and mechanical degrees of freedom: it is an eight node hexahedron. The stiffness matrix integrates the constitutive law from the four tangent operators given by the constitutive law. The non linear problem is solved by the Newtons method. This finite element tool is used to study the effects of applied voltage on the electroelastic field concentrations ahead of electrodes in a multilayer piezoelectric actuator. The study lies on the experimental observations made by Shindo et al. [1]. Electroelastic analysis on piezoceramics with surface electrode showed that high values of stress and electric displacement arose in the neighbourhood of the electrode tip. Thus, the strain, stress and electric displacement concentrations were calculated and the numerical results showed that ferroelectric switching arose in the area of the electrode tip, causing a change in remnant polarization and remnant strain.