An extended molecular statics algorithm simulating the electromechanical continuum response of ferroelectric materials

Molecular dynamics (MD) simulations of ferroelectric materials have improved tremendously over the last few decades. Specifically, the core-shell model has been commonly used for the simulation of ferroelectric materials such as barium titanate. However, due to the computational costs of MD, the calculation of ferroelectric hysteresis behaviour, and especially the stress-strain relation, has been a computationally intense task. In this work a molecular statics algorithm, similar to a finite element method for nonlinear trusses, has been implemented. From this, an algorithm to calculate the stress dependent continuum deformation of a discrete particle system, such as a ferroelectric crystal, has been devised. Molecular statics algorithms for the atomistic simulation of ferroelectric materials have been previously described. However, in contrast to the prior literature the algorithm proposed in this work is also capable of effectively computing the macroscopic ferroelectric butterfly hysteresis behaviour. Therefore the advocated algorithm is able to calculate the piezoelectric effect as well as the converse piezoelectric effect simultaneously on atomistic and continuum length scales. Barium titanate has been simulated using the core-shell model to validate the developed algorithm