Effective properties of cracked piezoelectrics with non-trivial crack face boundary conditions

Abstract

Effective elastic, dielectric and piezoelectric coefficients are crucial for modeling the constitutive behavior of piezo-and ferroelectric materials. A homogenization process provides the average properties of a representative volume element and allows for the mathematical treatment of boundary value problems within the context of classical continuum mechanics of homogeneous media. Cracks, in particular, have an impact on all these effective coefficients. A sophisticated model has to account for crack interaction as well as appropriate boundary conditions regarding electric charges and induced stresses on the crack faces. Results are obtained applying analytical homogenization approaches leading to closed-form solutions in the limiting case of non-interacting cracks.

Continuum damage model for ferroelectric materials and its application to multilayer actuators

“…The constitutive law, as given by equations ( 5) and (6) describes the relations between electric and mechanical fields in a ferroelectric body. However, in the presence of damage, the coupling is weakened and the material constants are significantly lowered [29,30]. Therefore, a general relation between the volume averages of two sets of piezoelectric field variables P and Z is considered as…”

“…those of an impermeable crack with charge-free faces, have been chosen for this paper. More sophisticated and thus physically more appropriate boundary conditions implicate a complex homogenization theory [30]. Equation (37) is drawn from a closed form solution of the piezoelectric Griffith crack problem [26,31], meaning that the crack is assumed to be in a flawless poled piezoelectric matrix medium.…”