A continuum theory for the thermomechanics of solidification

International Journal of Non-Linear Mechanics

Volumn 32, Issue 1, 1997, Pages 3-20

  Baldoni, F ^a   Rajagopal, K R ^a  

^a University of Pittsburgh   (United States)

Author keywords

Cauchy Green stretch tensor; Isotropy; Singular surface; Solidification; Symmetry group; Velocity gradient

Indexed keywords

ELASTICITY; FREEZING; GREEN'S FUNCTION; MATHEMATICAL MODELS; NEWTONIAN FLOW; TENSORS; THERMOMECHANICAL TREATMENT; VELOCITY;

THERMOMECHANICS;

SOLIDIFICATION;

EID: 0030737190     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-7462(96)00040-6     Document Type: Article

References (25)

1. J. Crank, Free and Moving Boundary Problems. Clarendon Press (1984).
2. A. Fasano and M. Primicerio, Freezing in porous media; a review of mathematical models. In Applications of Mathematics in Technology (edited V. Boffi and H. Neunzert), pp. 288-311. Teubner (1984).
3. G. Fix, Phase field model for free boundary problems. In Free Boundary Problems: Theory and Applications II (edited by A. Fasano and M. Primicerio), pp. 580-589. Pitman (1983).
4. G. Caginalp, An analysis of a phase field model of a free boundary. Arch. Rat. Mech. Anal. 93, 205 (1986).
5. P. C. Hohenberg and B. I. Halperlin. Theory of dynamic critical phenomena, Rev. Mod. Phys. 45, 435 (1977).
6. L. D. Landau, Collected Papers. Gordon and Breach (1967).
7. R. N. Hills, D. E. Loper and P. H. Roberts, A thermodynamically consistent model of a mushy zone. Quart. J. Mech. Appl. Math. 36, 505 (1983).
8. R. N. Hills and P. H. Roberts, On the formulation of diffusive mixture theory for two-phase region. J. Engng Math. 22, 93 (1988).
9. R. N. Hills and P. H. Roberts, A macroscopic model of phase coarsening. Int. J. Non-Linear Mech. 25, 319 (1990).
10. V. R. Voller, M. Cross and N. C. Markatos, An enthalpy method for convection/diffusion phase change. Int. J. Num. Meth. Engng 24, 271 (1987).
11. E. H. Stanley, Introduction to Phase Transitions and Critical Phenomena. Oxford University Press (1987).
12. K. R. Rajagopal and A. S. Wineman, A two network theory in non-linear elasticity. Arch. Mech. 42, 532 (1990).
13. A. S. Wineman and K. R. Rajagopal, A constitutive equation for non-linear elastic materials which undergo deformation induced micro structural changes. Int. J. Plasticity 8, 385 (1992).
14. A. V. Tobolsky and R. D. Andrews, Systems manifesting elastic and viscous behavior. J. Chem. Phys. 13, 3 (1945).
15. A. V. Tobolsky, R. D. Andrews and E. E. Hanson, The theory of permanent set at elevated temperatures in natural and synthetic rubber vulcanizates. J. Appl. Phys. 17, 352 (1946).
16. A. V. Tobolsky, I. B. Prettyman and J. H. Dillon, Stress relaxation of natural and synthetic rubber stocks. J. Appl. Phys. 15, 380 (1944).
17. A. Peterlin, Crystalisation from a strained melt or solution. Polymer Engng Sci. 16, 126 (1976).
18. K. R. Rajagopal and A. Srinivasa, On inelastic behavior of solids part 1: twinning. Int. J. Plasticity 11, 653 (1995).
19. B. D. Coleman and V. J. Mizel. Existence of caloric equations of state in thermodynamics. J. Chem. Phys. 40, 1116 (1964).
20. C. Truesdell and R. Toupin, The Classical Field Theories, Handbuch der Physik, vol. III/1. Springer-Verlag (1964).
21. L. D. Landau and E. M. Lifschitz, Statistical Physics, Course in Theoretical Physics, Vol. 5. Pergamon Press (1980).
22. A. B. Pippard, Elements of Classical Thermodynamics. Cambridge University Press (1957).
23. A. J. M. Spencer, Theory of Invariants. In Continuum Physics (edited by A. C. Eringen), Vol. 3, pp. 240-353. Academic Press (1975).
24. O. Richmond and R. H. Tien, Theory of thermal stresses and air-gap formation during the early stages of solidification in a rectangular mold. J. Mech. Phys. Sol. 19, 273 (1971).
25. P. Chadwick, Thermomechanics of rubberlike materials. Proc. R. Soc. Lond. A 276, 371 (1974).