Impact induced depolarization of ferroelectric materials

We study the large deformation dynamic behavior and the associated nonlinear electro-thermo-mechanical coupling exhibited by ferroelectric materials in adiabatic environments. This is motivated by a ferroelectric generator which involves pulsed power generation by loading the ferroelectric material with a shock, either by impact or a blast. Upon impact, a shock wave travels through the material inducing a ferroelectric to nonpolar phase transition giving rise to a large voltage difference in an open circuit situation or a large current in a closed circuit situation. In the first part of this paper, we provide a general continuum mechanical treatment of the situation assuming a sharp phase boundary that is possibly charged. We derive the governing laws, as well as the driving force acting on the phase boundary. In the second part, we use the derived equations and a particular constitutive relation that describes the ferroelectric to nonpolar phase transition to study a uniaxial plate impact problem. We develop a numerical method where the phase boundary is tracked but other discontinuities are captured using a finite volume method. We compare our results with experimental observations to find good agreement. Specifically, our model reproduces the observed exponential rise of charge as well as the resistance dependent Hugoniot. We conclude with a parameter study that provides detailed insight into various aspects of the problem.