To simulate the nonlinear behavior of ferroelectric structures and devices under non-uniform electromechanical loadings,a domain-switching embedded electromechanical finite element method is developed in this paper.Following continuum assumption,the electromechanical behavior of each representative material point can be obtained by averaging the behavior of the local corresponding microstructure,e.g.42 domains used in this work.A new Double Gibbs free energy criterion for domain-switching is proposed to ensure the convergence and stability of the simulations on ferroelectrics under non-uniform field.Several computational examples are given to demonstrate that this nonlinear finite element method can yield reasonable and stable simulation results which can be used to explain some experimental results and assist the design of ferroelectric devices.
How to correctly extract Cauchy stress from the atomistic simulations is a crucial issue in studying the mechanical behaviours of atomic systems, but is still in controversy. In this paper, three typical atomistic simulation examples are used to validate various existing stress definitions. It is found that the classical virial stress fails in predicting the stresses in these examples, because the velocity depends on the choice of the local average volume or the reference frame velocity and other factors. In contrast, the Lagrangian cross-section stress and Lagrangian virial stress are validated by these examples, and the instantaneous Lagrangian atomic stress definition is also proposed for dynamical problems.
