| Within a thermomechanical framework which includes the effects of viscosity, heat conduction and interstitial working, I investigate the phenomenon of sonically propagating phase boundaries in one-dimensional solid bodies possessing a nonconvex Helmholtz free energy. The constitutive structure of the material is similar to a model devised by FALK (Model free energy, mechanics, and thermodynamics of shape memory alloys. Acta Metallurgica, 28:1773--1780, 1980) to model first order martensitic phase transformations, but the thermomechanical framework is that of DUNN & S ERRIN (On the thermomechanics of interstitial working. Archive for Rational Mechanics and Analysis, 88:95--133, 1985) and D UNN (Interstitial working and a nonclassical continuum thermodynamics. In Serrin, editor, New Perspectives Ire Thermodynamics, Springer-Verlag, 1986, pages 187--222). Following the example of AFFOUF & CAFLISCH (A numerical study of Riemann problem solutions and stability for a system of viscous conservation laws of mixed type. SIAM Journal on Applied Mathematics, 51:605--634, 1991), a numerical scheme for solving the coupled nonlinear partial differential equations is devised and then utilized to argue for the plausibility of sonically propagating phase boundaries in a limiting case. |
