Dynamic phase-field modeling of rate-dependent irreversible-to-reversible transition: Electro-mechanical erasure of force-induced phase transition in relaxor ferroelectric PMN-PT

Understanding the phase-transition dynamics of relaxor ferroelectrics under coupled electro-mechanical fields is key for advanced electromechanical devices, yet mechanisms of mechanically induced irreversible transitions and non-equilibrium responses across strain rates remain elusive. Here, we develop a modified dynamic phase-field model incorporating a higher-order time-derivative term of polarization (parameter μ) and stiffness-damping term for mechanical equilibrium (parameter β) to systematically investigate the coupled electro-mechanical behavior in PMN-PT single crystals over a wide strain-rate range. The parameter β governs the rate-dependent decrease of critical transition load with decreasing strain rate, while μ primarily affects initial polarization oscillations under ultrafast loading with negligible influence on typical-rate kinetics. Using this model, we predict and reveal a reversible rhombohedral → tetragonal → rhombohedral transition pathway under electro-mechanical synergy. Nanoindentation induces an R → T transition that leaves a stable residual imprint after unloading (“mechanical write”). Subsequently, a localized electric field opposite to the indentation direction overcomes the energy barrier and drives a T → R back-transition (“electrical erase”), manifesting as a shape-memory characteristic in the macroscopic load–displacement curve. This study clarifies the physical roles of key parameters in dynamic phase-field modeling and unveils the dynamical mechanism of reversible phase-transition control in relaxor ferroelectrics from domain evolution and energetics perspectives, providing a theoretical foundation for designing novel phase-structure-based ferroelectric memory devices.