Configurational forces in ferroelectric structures analyzed by a macromechanical switching model

Polycrystalline ferroelectric ceramics are widely used in sensors, actuators, microelectromechanical systems, etc. If a ferroelectric structure possesses some defects like voids or inhomogeneities, its reliability is reduced, and undesired non-homogeneous local concentrations of the electromechanical fields occur. Under the applied external loading, a domain switching region evolves in the vicinity of defects, which is manifested as a reorientation of the remanent polarization vector. In the current work, the nonlinear electromechanical behavior of ferroelectric ceramics is computed by means of three-dimensional finite element analysis, using the phenomenological continuum mechanics model suggested by Landis (J. Mech. Phys. Solids 50(1):127–152, 2002. https://doi.org/10.1016/s0022-5096(01)00021-7) and numerically implemented by Stark (Int. J. Solids Struct. 80:359–367, 2015. https://doi.org/10.1016/j.ijsolstr.2015.09.004). This constitutive law is combined with user-developed elements in Abaqus commercial code for nonlinear coupled electromechanical analyses. By use of the numerical simulations, the evolution of all field variables, in particular of the polarization, is tracked. In a post-processing step, the configurational forces are computed, which express the thermodynamic driving forces acting on the defect. As a typical defect, we consider a circular void in the ferroelectric structure exposed to an alternating electric field. Additionally to the void, other inhomogeneities, namely, a strip of dissimilar material as well as dielectric and piezoelectric inclusions, are investigated. For all cases, the redistribution and evolution of the configurational forces are studied. Besides the essential findings and methodology achieved in this work, the developed software can serve as a basis for further investigations on the failure of composite smart structures and explicit crack modeling using fracture mechanical concepts.