Stick-slip interface motion as a singular limit of the viscosity-capillarity model

This work is a follow-up on a study by Vainchtein and Rosakis of interface dynamics and hysteresis in materials undergoing solid-solid phase transitio ns. The author investigates the dynamics of a bar with a nonconvex double-w ell elastic energy density. The model includes both viscosity and strain-gr adient capillarity terms. Viscous stress provides energy dissipation. The c apillarity term models interfacial energy. The bar is subject to time-depen dent displacement boundary conditions. Numerical simulations predict hyster etic behavior in the overall load-elongation diagram. The hysteresis is pri marily due to metastability and persists even at very slow loading when vis cous dissipation is small. At a given loading, a large capillarity coeffici ent alpha results in a smooth interface motion and small hysteresis loop. A s alpha becomes smaller, the loop grows and acquires serrations, while the interface motion alternates between slow and fast regimes. The results sugg est that the stick-slip interface motion and serrated hysteresis loop predi cted by Vainchtein and Rosakis in the absence of interfacial energy are a s ingular limit of the viscosity-capillarity model as the capillarity coeffic ient tends to zero. The irregular interface motion and serrated load-elonga tion curves qualitatively agree with some experimental observations in shap e-memory alloys.