Uncertainty Analysis of Ferroelectric Polydomain Structures

Ferroelectric materials exhibit strong electromechanical behavior which has led to the production of a wide variety of adaptive structures and intelligent systems, ranging from structural health monitoring sensors, energy harvesting circuits, and flow control actuators. Given the large number of applications, accurate prediction of ferroelectric materials constitutive behavior is critical. This presents many challenges, including the need to predict behavior from electronic structures up to macroscropic continuum. Many of the structure-property relations in these materials can be accurately calculated using density functional theory (DFT). However, DFT is not necessarily conducive to the large scale computations required to solve these problems on a continuum scale. Introducing a phase field polarization order parameter is an alternative approach, which provides a means to simulate the length scale gap between nano- and microscale domain structure evolution. The introduction of the phase field approximation results in uncertainty. Bayesian statistical analysis is an ideal tool for quantifying the uncertainty associated with the continuum phase field model parameters. Analyses of monodomain structures allows for identification of Landau energy and electrostrictive stress parameters. Identifying the exchange parameters, which are proportional to the polarization gradients, requires consideration of polydomain structures. This is a nontrivial problem as domain wall structures are fully coupled between the Landau energy, electrostrictive, and exchange parameters. Accurately quantifying the uncertainty in the phase field parameters will provide insight into the nonlinear constitutive behavior.