Unstable kinetic relations and the dynamics of solid-solid phase transitions

Journal of the Mechanics and Physics of Solids

Volumn 45, Issue 11-12, 1997, Pages 2055-2081

  Rosakis, Phoebus ^a   Knowles, James K ^b  

^a Department of Obstetrics Gynecology   (United States)

^b California Institute of Technology   (United States)

Author keywords

A. acoustics; A. phase transformation; A. shock waves; B. stress waves; C. stability and bifurcation

Indexed keywords

ACOUSTIC EMISSIONS; BIFURCATION (MATHEMATICS); MATHEMATICAL MODELS; SHOCK WAVES;

SOLID-SOLID PHASE TRANSITIONS;

PHASE TRANSITIONS;

EID: 0031277176     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(97)00026-4     Document Type: Article

References (21)

1. Abeyaratne, R., Chu, C. and James, R. D. (1996) Kinetics of materials with wiggly energies: theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape-memory alloy. Philosophical Magazine 73, 457-497.
2. Abeyaratne, R. and Knowles, J. K. (1990) 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.
3. Abeyaratne, R. and Knowles, J. K. (1991) Kinetic relations and the propagation of phase boundaries in solids. Archive for Rational Mechanics and Analysis 114, 119-154.
4. Abeyaratne, R. and Knowles, J. K. (1992a) Nucleation, kinetics and admissibility criteria for propagating phase boundaries. In Shock Induced Transitions and Phase Structures in General Media, ed. E. Dunn, R. Fosdick and M. Slemrod. IMA Volumes in Mathematics and its Applications, Vol. 52, pp. 1-33. Springer, Berlin.
5. Abeyaratne, R. and Knowles, J. K. (1992b) Reflection and transmission of waves from an interface with a phase-transforming solid. Journal of Intelligent Material Systems and Structures 3, 224-244.
6. Abeyaratne, R. and Knowles, J. K. (1997) Impact-induced phase transitions in thermoelastic solids. Philosophical Transactions of the Royal Society 355, 843-867.
7. Chang, L.-C. (1952) On diffusionless transformation in Au-Cd single crystals containing 47.5 atomic per cent cadmium: characteristics of single-interface transformation. Journal of Applied Physics 23, 725-728.
8. Devaney, R. L. (1986) An Introduction to Classical Dynamical Systems. Benjamin/Cummings, Menlo Park, CA.
9. Ericksen, J. L. (1975) Equilibrium of bars. Journal of Elasticity 5, 191-201.
10. Fowles, G. R. (1976) Conditional stability of shock waves - a criterion for detonation. Physics of Fluids 19, 227-238.
11. Fried, E. (1992) Stability of a two-phase process involving a planar phase boundary in a thermoelastic solid. Continuum Mechanics and Thermodynamics 4, 59-79.
12. Fried, E. (1993a) Construction of two-phase equilibria in a non-elliptic hyperelastic solid. Journal of Elasticity 31, 71-123.
13. Fried, E. (1993b) Stability of a two-phase process in an elastic solid. Journal of Elasticity 31, 163-187.
14. Krishnan, R. V. (1985) Stress induced martensitic transformations. Materials Science Forum 3, 387-398.
15. Ngan, S.-C. and Truskinovsky, L. (1996) Kinetic relations for adiabatic phase boundaries. Preprint.
16. Owen, W. S., Schoen, F. J. and Srinivasan, G. R. (1970) The growth of a plate of martensite. In Phase Transformations, ed. H. I. Aaronson, pp. 157-180. American Society of Metals, Metals Park, OH.
17. Pence, T. J. (1987) Formulation and analysis of a functional equation describing a moving one-dimensional elastic phase boundary. Quarterly of Applied Mathematics 45, 293-304.
18. Rosakis, P. (1995) An equal area rule for dissipative kinetics of propagating strain discontinuities. SIAM Journal on Applied Mathematics 55, 100-123.
19. Turteltaub, S. (1997) Viscosity and strain gradient effects on the kinetics of propagating phase boundaries in solids. Journal of Elasticity 46, 53-90.
20. Zhong, X. (1995) Dynamic behavior of the interface between two solid phases in an elastic bar. Journal of Elasticity 41, 39.
21. Zhong, X., Hou, T. Y. and Lefloch, P. G. (1996) Computational methods for propagating boundaries. Journal of Computational Physics 124, 192.