Macroscopic constitutive model for ergodic and non-ergodic lead-free relaxors

A fully electromechanically coupled, three dimensional phenomenological constitutive model for relaxor ferroelectric materials was developed for the use in a finite-element-method (FEM) solution procedure. This macroscopic model was used to simulate the macroscopic electromechanical response of lead-free ergodic 0.94Na1/2Bi1/2TiO3−0.06BaTiO3 and non-ergodic 0.90Na1/2Bi1/2TiO3−0.06BaTiO3−0.04K0.5Na0.5NbO3 relaxor materials. The presented constitutive model is capable of accounting for the observed pinched hysteretic response as well as non-deviatoric polarization induced strain and internal order transitions. Time integration of the history dependent internal variables is done with a predictor-corrector integration scheme. The adaptability of the constitutive model regarding the pinching of the hystereses is shown. Simulations are compared to experimental observations.