Abstract
An Eulerian expression for the dissipation due to a moving surface of discontinuity in mass density, velocity, stress, energy, and heat flux is obtained. This leads to Eulerian measures forenergy release andfriction — measures that are work conjugate tomass flux andvelocity slip, respectively. Constitutive equations involving these quantities are proposed as a means to determine transition kinetics in materials that change phase.
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Abeyaratne, R.; Knowles, J.K.: On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solids 38 (1990), 345–360
Knowles, J.K: On the dissipation associated with equilibrium shocks in finite elasticity. Journal of Elasticity 9 (1979), 131–158
Heidug, W.; Lehner, F.K.: Thermodynamics of coherent phase transformations in nonhydrostatically stressed solids. Pure Appl. Geophys. 123 (1985), 91–98
Truskinovsky, L.M.: Dynamics of nonequilibrium phase boundaries in a heat conducting non-linearly elastic medium. J. Appl. Math. Mech. 51 (1987), 777–784
Truskinovsky, L.M.: Kinks versus shocks. In: Shock Induced Transitions and Phase Structures in General Media, (J.E. Dunn, R. Fosdick, M. Slemrod, eds.). SpringerVerlag, Berlin, 1992
Chadwick, P.: Continuum Mechanics: Concise Theory and Problems. Wiley, New York, 1976
Courant, R.; Friedrichs, K.O.: Supersonic Flow and Shock Waves. Interscience, New York, 1948
Pippard, A.B.: Classical Thermodynamics. Cambridge University Press, Cambridge, 1957
Eshelby, J.D.: Energy relations and the energy-momentum tensor in continuum mechanics. In: Inelastic Behavior of Solids, (M.F. Kanninen, W.F. Alder, A.R. Rosefield, R.I. Jaffe, eds.). McGraw-Hill, New York, 1970
Eshelby, J.D.: The elastic energy-momentum tensor. J. Elast. 5 (1975), 321–335
Chadwick, P.: Applications of the energy-momentum tensor in non-linear elastostatics. J. Elast. 5 (1975), 249–258
Kamb, B.: The thermodynamic theory of non-hydrostatically stressed solids. J. Geophys. Res. 66 (1961) 259–271
Grinfeld, M.: Phase transitions of the first kind in nonlinear-elastic materials. Mech. Solids 17 (1982) 92–101
Hutter, K.: Theoretical Glaciology. Reidel, Dordrecht, 1983
Truesdell, C.: Rational Thermodynamics. McGraw-Hill, New York, 1969
Abeyaratne, R; Knowles, J.K.: On the dissipative response due to discontinuous strains in bars of unstable elastic material. Int. J. Solids Struct. 24 (1988), 1021–1044
Abeyaratne, R; Knowles, J.K.: Unstable elastic materials and the viscoelastic response of bars in tension. J. Appl. Mech. 55 (1988), 491–492
Abeyaratne, R; Knowles, J. K.: Kinetic relations and the propagation of phase boundaries in solids. Arch. Rational Mech. Anal. 114 (1991), 119–154
Fried, E; Milic, N.: Phase transitions in fluids of van der Waals type. (Forthcoming)
de Groot, S.R.; Mazur, P.: Non-Equilibrium Thermodynamics. North-Holland, Amsterdam, 1962
Gurtin, M.E.: Multiphase thermomechanics with interfacial structure — 1. Heat conduction and the capillary balance law. Arch. Rational Mech. Anal. 104 (1988), 195–221
Gurtin, M.E.: A mechanical theory for the crystallization of a rigid solid in a liquid melt; melting-freezing waves. Arch. Rational Mech. Anal. 110 (1990), 287–312
Gurtin, M.E.; Struthers, A.: Multiphase thermomechanics with interfacial structure — 3. Evolving phase boundaries in the presence of bulk deformation. Arch. Rational Mech. Anal. 112 (1990), 97–160
Gurtin, M.E.: The dynamics of solid-solid phase transitions — 1. Coherent transitions. Arch. Rational Mech. Anal. 123 (1990), 305–335
Cermelli, P; Gurtin, M.E.: unpublished notes
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Fried, E. Energy release, friction, and supplemental relations at phase interfaces. Continuum Mech. Thermodyn 7, 111–121 (1995). https://doi.org/10.1007/BF01175772
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DOI: https://doi.org/10.1007/BF01175772