Macroscopic constitutive model for ergodic and non-ergodic lead-free relaxors. (May 2022) - Streich, Friedemann A; Martin, Alexander; Webber, Kyle G; Kamlah, Marc
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 ergodic0 . 94 N a 1 / 2 B i 1 / 2 Ti O 3 − 0 . 06 BaTi O 3 and non-ergodic0 . 90 N a 1 / 2 B i 1 / 2 Ti O 3 − 0 . 06 BaTi O 3 − 0 . 04 K 0 . 5 N a 0 . 5 Nb O 3 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.