Domain engineered ferroelectric relaxor-PT crystals have attracted extensive attentions due to their ultrahigh piezoelectric coefficients and electromechanical coupling factors. To gain insight into the microstructure and its effects on the material behavior, a modeling approach was developed from an energetic perspective. A Landau-Devonshire energy function, in the form of a 10th order polynomial, was proposed to describe the dielectric, piezoelectric and ferroelectric properties of rhombohedral phase PIN-PMN-PT crystals with a MPB composition. The coefficients of this energy function were determined through extensive fitting to the experimental data. The resulting energy function reproduced the temperature induced phase transformations as well as the polarization and strain hysteresis loops of domain engineered 4R and 2R crystals. This energy function was then implemented in a phase-field model to investigate the evolution of domain structures under the electric field. A new way to apply periodic boundary conditions was implemented to accommodate nonzero strain during domain formation and evolution. The domain formation process was simulated first and 71 and 109 domain walls were found to populate the crystals. Then these two types of domain walls were individually studied under the electric field applied along the [110] direction. They showed different behavior in response to the electric field. A domain wall broadening effect was observed on 71 domain walls when below the coercive field. When the field exceeded the coercive field, homogeneous polarization switching occurred with no motion of 71 domain walls. While the sweeping of 109 domain walls facilitated heterogeneous polarization switching and reduced the energy required relative to homogeneous polarization switching. The two mechanisms of domain evolution are consistent with the minimal domain wall motion in the engineered domain structures under the electric field. With this work, the application of the phase-field method was expanded to the new rhombohedral phase relaxor-PT crystals beyond ferroelectric materials with tetragonal symmetry. This work also deepened the understanding of domain structures of ferroelectric single crystals that is important in many applications.