The stress and strain properties of $\langle 001 \rangle$ oriented PMN-0.32PTrelaxor ferroelectric single crystals have been investigated. Obtainedresults show that the stress and strain behavior along $\langle 001 \rangle$crystallographic direction is different from that of the ferroelectricpolycrystal. Polarization rotation models are developed to explain theobserved behaviors of PMN-0.32PT. Based on the experimental phasetransformation mechanism of ferroelectric single crystal, a constitutivemodel of ferroelectric single crystal is proposed based micromechanicalmethod. In the model, the phase transformation systems on 8 possible slidingplanes are characterized by a viscoplastic law. The behavior offerroelectric single crystal is then derived from phenomenalcrystallographic theory through the transformation strain on sliding planes.The developed model has been applied to simulate the experimentalstress-strain curve of $\langle 001 \rangle$ oriented PMN-0.32PT. It is shown that thedeveloped model can faithfully capture the key characteristic of theobserved constitutive behavior of $\langle 001 \rangle$ oriented PMN-0.32PT.