Development of a Ferroelectric Shell Finite Element
Ferroelectricity is the non-linear behaviour exhibited by piezoelectric ceramics, especially in the application of high electric field. Actually, the demand for numerical tools taking into account this non linear phenomenon is increasing to reliably design applications using piezoelectric ceramics. In this context, a shell finite element based on the Reissner/Mindlin's theory and integrating a bi-dimensional macroscopic constitutive law for domain switching effects (ferroelectricity) is developed. This element is implemented into the finite element code ABAQUS using the subroutine UEL (User ELement). The thermodynamical framework of the law is based on two scalar valued functions: the Helmoltz free energy and an electric switching function. One internal variable (the remanent polarization) is introduced and a non linear switching effect hardening is considered. An implicit integration of the constitutive equations based on the return-mapping algorithm is developed.
Pietro VINCENZINI and Fabio CASCIATI
W. Zouari et al., "Development of a Ferroelectric Shell Finite Element", Advances in Science and Technology, Vol. 56, pp. 57-63, 2008