An optimization-based computational model for domain evolution in polycrystalline ferroelastics

An optimization-based computational model is proposed to study domain evolution in polycrystalline ferroelastics composed of numerous randomly oriented grains, each of which consists of multiple types of domains. Under any prescribed loading, the volume fraction of each domain in a grain is obtained by minimizing the free energy of the said grain using an optimization method. The mechanical constraint from the neighboring grains is considered using Eshelby inclusion approach. This model has the similar superiority as the phase field model, which does not require imposition of any priori domain-switching criterion. The computational efficiency of this model is fairly high and it is feasible to study three-dimensional cases using numerous grains. Furthermore, this model can reproduce Taylor’s rule of plasticity very well. Simulation results for tetragonal, rhombohedral and morphotropic PZT ceramics are employed to validate the superiority and efficiency of this model. The domain texture evolution process can also be calculated.