Continuum models for irregular phase boundary motion in shape-memory tensile bars

We consider quasi-static displacement-controlled loading through one stress cycle of a shape-memory tensile bar modeled as a one-dimensional, two-phas e elastic solid. Our objective is to explore the effect on the associated h ysteresis loop of various qualitatively different types of kinetic relation s, bearing in mind certain features of such loops that have been observed e xperimentally. We show that when the model involves a kinetic relation that is 'unstable' in a definite sense, 'stick-slip' motion of the interface be tween phases and serration of the accompanying stress-elongation curve are both predicted at slow elongation rates. We also show that a 'nonhomogeneou s' kinetic relation intended to model the effect of micro-obstacles on inte rface motion also leads to irregular interface motion and a serrated stress -elongation curve, in this case at all elongation rates. (C) Elsevier, Pari s.