(Adiabatic) phase boundaries in a bistable chain with twist and stretch

Abstract

Mass–spring chains with only extensional degrees of freedom have provided insights into the behavior of crystalline solids, including those capable of phase transitions. Here we add rotational degrees of freedom to the masses in a chain and study the dynamics of phase boundaries across which both the twist and stretch can jump. We solve impact and Riemann problems in the chain by numerical integration of the equations of motion and show that the solutions are analogous to those in a phase transforming rod whose stored energy function depends on both twist and stretch. From the dynamics of phase boundaries in the chain we extract a kinetic relation whose form is familiar from earlier studies involving chains with only extensional degrees of freedom. However, for some combinations of parameters characterizing the energy landscape of our springs we find propagating phase boundaries for which the rate of dissipation, as calculated using isothermal expressions for the driving force, is negative. This suggests that we cannot neglect the energy stored in the oscillations of the masses in the interpretation of the dynamics of mass–spring chains. Keeping this in mind we define a local temperature of our chain and show that it jumps across phase boundaries, but not across sonic waves. Hence, impact problems in our mass–spring chains are analogous to those on continuum thermoelastic bars with Mie–Gruneisen type constitutive laws. At the end of the paper we use our chain to shed some light on experiments involving yarns that couple twist and stretch to perform useful work in response to various stimuli.