Hysteresis and stick-slip motion of phase boundaries in dynamic models of phase transitions

We investigate hysteretic behavior in two dynamic models for solid-solid ph ase transitions. An elastic bar with a nonconvex double-well elastic energy density is subjected to time-dependent displacement boundary conditions. B oth models include inertia and a viscous stress term that provides energy d issipation. The first model involves a strain-gradient term that models int erfacial energy. In the second model this term is omitted. Numerical simula tions combined with analytical results predict hysteretic behavior in the o verall end-load versus end-displacement diagram for both models. The hyster esis is largely due to metastability and nucleation; it persists even for v ery slow loading when viscous dissipation is quite small. In the model with interfacial energy, phase interfaces move smoothly. When this term is omit ted, hysteresis is much more pronounced. In addition, phase boundaries move in an irregular, stick-slip fashion. The corresponding load-elongation cur ve exhibits serrations, in qualitative agreement with certain experimental observations in shape-memory alloys.