Configurational Forces in Continuous Theories of Elastic Ferroelectrics

Abstract

Domain walls in a ferroelectric crystal are considered as sharp interfaces, so their motion is governed by field equations, jump conditions and an appropriate kinetic relation between the domain wall velocity and the driving force. In this article, a regularized version of the sharp-interface theory in ferroelectrics is presented, by introducing a level set function that changes sign from domain to domain smoothly and thus eliminating discontinuities. It is proved that considering level set functions as constitutive variables in the energy functional, the driving forces that move domain walls are configurational forces obeying the canonical momentum equation. A new, recently proposed differential equation is used to describe the evolution of the level set function which keeps level set function closer to a signed distance function as possible. Theoretical considerations and numerical simulations show that configurational forces are closely related to the level set description of sharp interface theories in solids. Moreover, it is displayed that in-homogeneity forces drive the system successfully to the typical domain structure of elastic ferroelectrics.