The dynamical aspects of solid-solid phase transformations are studied within the framework of the theory of thermoelasticity. A problem of the Riemann type for a one-dimensional bar undergoing an adiabatic process is analyzed. It is shown that by imposing a kinetic relation and a nucleation criterion, it is possible to single out a unique solution. This extends to the thermomechanical case results previously found in a purely mechanical context.
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References
1.
[1] Abeyaratne, R. and Knowles, J. K.: On the driving traction acting on a surface of strain discontinuity in a continuum. Journal of the Mechanics and Physics of Solids, 38, 345-360 (1990).
2.
[2] Abeyaratne, R. and Knowles, J. K.: A continuum model of a thermoelastic solid capable of undergoing phase transitions. Journal of the Mechanics and Physics of Solids, 41, 541-571 (1993).
3.
[3] Abeyaratne, R. and Knowles, J. K.: Kinetic relations and the propagation of phase boundaries in solids. Archive for Rational Mechanics and Analysis, 114, 119-154 (1991).
4.
[4] Abeyaratne, R. and Knowles, J. K.: Dynamics of propagating phase boundaries: Adiabatic theory for thermoelastic solids. Physica D, 79, 269-288 (1994).
5.
[5] Callen, H. B.: Thermodynamics and an Introduction to Thermostatistics, 2nd ed., John Wiley, New York, 1985.
6.
[6] Christian, J. W.: The Theory of Transformations in Metals and Alloys, 2d ed., Pergamon, New York, 1981.
7.
[7] Shearer, M.: Nonuniqueness of admissible solutions of Riemann initial value problems for a system of conservation laws of mixed type. Archive for Rational Mechanics and Analysis, 93, 45-59 (1986).
8.
[8] Slemrod, M.: A limiting "viscosity" approach to the Riemann problem for materials exhibiting change of phase. Archive for Rational Mechanics and Analysis, 105, 327-365 (1989).
9.
[9] Truesdell, C.: Rational Thermodynamics, 2d ed., Springer-Verlag, New York, 1984.
10.
[10] Truskinovsky, L.: Kinks versus shocks, in Shock Induced Transitions and Phase Structures in General Media, pp.185-229 eds., R. Fosdick, E. Dunn, and M. Slemrod, Springer-Verlag, New York, 1993.
