Kinetics of martensitic phase transitions: Lattice model

SIAM Journal on Applied Mathematics

Volumn 66, Issue 2, 2006, Pages 533-553

  Truskinovsky, Lev ^a   Vainchtein, Anna ^b  

^a LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

^b UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Driving force; Lattice models; Lattice waves; Martensitic phase transitions; Nonlocal interactions; Radiative damping

Indexed keywords

DRIVING FORCE; LATTICE MODELS; LATTICE WAVES; MARTENSITIC PHASE TRANSITIONS; NONLOCAL INTERACTIONS; RADIATIVE DAMPING;

COMPUTER SIMULATION; ENTROPY; HAMILTONIANS; INITIAL VALUE PROBLEMS; MICROSTRUCTURE; PHASE TRANSITIONS;

MARTENSITIC TRANSFORMATIONS;

EID: 33645776187     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040616942     Document Type: Article

References (37)

1. R. ABEYARATNE AND J. KNOWLES, A continuum model of a thermoelastic solid capable of undergoing phase transitions, J. Mech. Phys. Solids, 41 (1993), pp. 541-571.
2. W. ATKINSON AND N. CABRERA, Motion of a Frenkel-Kontorova dislocation in a one-dimensional crystal, Phys. Rev. A, 138 (1965), pp. 763-766.
3. O. M. BRAUN AND Y. S. KIVSHAR, Nonlinear dynamics of the Frenkel-Kontorova model, Phys. Rep., 306 (1998), pp. 1-108.
4. O. M. BRAUN, Y. S. KIVSHAR, AND I. I. ZELENSKAYA, Kinks in the Frenkel-Kontorova model with long-range interparticle interactions, Phys. Rev. B, 41 (1990), pp. 7118-7138.
5. A. CARPIO AND L. L. BONILLA, Oscillatory wave fronts in chains of coupled nonlinear oscillators, Phys. Rev. E, (2003), p. 056621.
6. V. CELLI AND N. FLYTZANIS, Motion of a screw dislocation in a crystal, J. Appl. Phys., 41 (1970), pp. 4443-4447.
7. C. M. DAFERMOS, Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, Heidelberg, 2000.
8. J. ERICKSEN, Equilibrium of bars, J. Elasticity, 5 (1975), pp. 191-202.
9. Y. GAIDIDEIB, N. FLYTZANIS, A. NEUPERA, AND F. G. MERTENSA, Effect of non-local interactions on soliton dynamics in anharmonic chains: Scale competition, Phys. D, 107 (1997), pp. 83-111.
10. T. Y. HOU AND P. LAX, Dispersive approximations in fluid dynamics, Comm. Pure Appl. Math., 44 (1991), pp. 1-40.
11. O. KRESSE AND L. TRUSKINOVSKY, Mobility of lattice defects: Discrete and continuum approaches, J. Mech. Phys. Solids, 51 (2003), pp. 1305-1332.
12. O. KRESSE AND L. TRUSKINOVSKY, Lattice friction for crystalline defects: From dislocations to cracks, J. Mech. Phys. Solids, 52 (2004), pp. 2521-2543.
13. P. G. LEFLOCH, Hyperbolic Systems of Conservation Laws, ETH Lecture Note Series, Birkhäuser, Boston, 2002.
14. M. MARDER AND S. GROSS, Origin of crack tip instabilities, J. Mech. Phys. Solids, 43 (1995), pp. 1-48.
15. R. D. MINDLIN, Second gradient of strain and surface tension in linear elasticity, Internat. J. Solids Structures, 1 (1965), pp. 417-438.
16. S.-C. NGAN AND L. TRUSKINOVSKY, Thermal trapping and kinetics of martensitic phase boundaries, J. Mech. Phys. Solids, 47 (1999), pp. 141-172.
17. S.-C. NGAN AND L. TRUSKINOVSKY, Thermo-elastic aspects of dynamic nucleation, J. Mech. Phys. Solids, 50 (2002), pp. 1193-1229.
18. M. PEYHARD, Simple theories of complex lattices, Phys. D, 123 (1998), pp. 403-424.
19. M. PEYRARD, S. PNEVMATIKOS, AND N. FLYTZANIS, Discreteness effects on non-topological kink soliton dynamics in nonlinear lattices, Phys. D, 19 (1986), pp. 268-281.
20. D. SERRE, Systems of Conservation Laws, vols. 1, 2, Cambridge University Press, Cambridge, UK, 1999.
21. M. SLEMROD, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Ration. Mech. Anal., 81 (1983), pp. 301-315.
22. L. I. SLEPYAN, Dynamics of a crack in a lattice, Soviet Phys. Dokl., 26 (1981), pp. 538-540.
23. L. I. SLEPYAN, The relation between the solutions of mixed dynamical problems for a continuous elastic medium and a lattice, Soviet Phys. Dokl., 27 (1982), pp. 771-772.
24. L. I. SLEPYAN, Models and Phenomena in Fracture Mechanics, Springer-Verlag, New York, 2002.
25. L. I. SLEPYAN, A. CHERKAEV, AND E.CHERKAEV, Transition waves in bistable structures. II. Analytical solution: wave speed and energy dissipation, J. Mech. Phys. Solids, 53 (2005), pp. 407-436.
26. L. I. SLEPYAN AND L. V. TROYANKINA, Fracture wave in a chain structure, J. Appl. Mech. Tech. Phys., 25 (1984), pp. 921-927.
27. M. TODA, Theory of nonlinear lattices, Springer-Verlag, Berlin, 1989.
28. N. TRIANTAFYLLIDIS AND S. BARDENHAGEN, The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models, J. Mech. Phys. Solids, 44 (1996), pp. 1891-1928.
29. L. TRUSKINOVSKY, Equilibrium interphase boundaries, Soviet Phys. Dokl., 27 (1982), pp. 306-331.
30. L. TRUSKINOVSKY, Dynamics of nonequilibrium phase boundaries in a heat conducting elastic medium, J. Appl. Math. Mech., 51 (1987), pp. 777-784.
31. L. TRUSKINOVSKY, Kinks versus shocks, in IMA Series in Mathematics and Its Applications, E. D. R. Fosdick and M. Slemrod, eds., Vol. Math. Appl. 52, Springer-Verlag, 1993, pp. 185-229.
32. L. TRUSKINOVSKY AND A. VAINCHTEIN, Peierls-Nabarro landscape for martensitic phase transitions, Phys. Rev. B, 67 (2003), p. 172103.
33. L. TRUSKINOVSKY AND A. VAINCHTEIN, The origin of nucleation peak in transformational plasticity, J. Mech. Phys. Solids, 52 (2004), pp. 1421-1446.
34. L. TRUSKINOVSKY AND A. VAINCHTEIN, in preparation.
35. L. TRUSKINOVSKY AND A. VAINCHTEIN, Explicit kinetic relation from "first principles," in Advances in Mechanics and Mathematics, vol. 11, P. Steinmann and G. Maugin, eds., Springer, New York, 2005.
36. L. TRUSKINOVSKY AND A. VAINCHTEIN, Quasicontinuum modeling of short-wave instabilities in crystal lattices, Philosophical Magazine, to appear.
37. L. TRUSKINOVSKY AND A. VAINCHTEIN, Quasicontinuum models of dynamic phase transitions, Continuum Mechanics and Thermodynamics, submitted.