Hierarchical pattern formation in elastic materials

Physica A: Statistical Mechanics and its Applications

Volumn 239, Issue 1-3, 1997, Pages 18-34

  Saxena, A ^a   Wu, Y ^b   Lookman, T ^b   Shenoy, S R ^c,d   Bishop, A R ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

^c UNIVERSITY OF HYDERABAD   (India)

^d ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

HIERARCHICAL SYSTEMS; MARTENSITIC TRANSFORMATIONS; MATERIALS SCIENCE; MATHEMATICAL MODELS;

BRANCHED TWINS; ELASTIC MATERIALS; GINZBURG-LANDAU THEORY;

ELASTICITY;

EID: 0031145503     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(96)00469-4     Document Type: Article

References (57)

1. C.M. Wayman, Introduction to the Theory of Martensitic Transformations (Macmillan, London, 1964).
2. L.E. Tanner, A.R. Pelton and R. Gronsky, J. Phys. (Paris) 43 (1982) C4-169; P.C. Clapp, J. Rifkin, J. Kenyon and L.E. Tanner, Metall. Trans. A 19 (1988) 783; R. Oshima, M. Sugiyama and F.E. Fujita, Metall. Trans. A 19 (1988) 803.
3. L.E. Tanner, A.R. Pelton and R. Gronsky, J. Phys. (Paris) 43 (1982) C4-169; P.C. Clapp, J. Rifkin, J. Kenyon and L.E. Tanner, Metall. Trans. A 19 (1988) 783; R. Oshima, M. Sugiyama and F.E. Fujita, Metall. Trans. A 19 (1988) 803.
4. L.E. Tanner, A.R. Pelton and R. Gronsky, J. Phys. (Paris) 43 (1982) C4-169; P.C. Clapp, J. Rifkin, J. Kenyon and L.E. Tanner, Metall. Trans. A 19 (1988) 783; R. Oshima, M. Sugiyama and F.E. Fujita, Metall. Trans. A 19 (1988) 803.
5. M. Sugiyama, Ph.D. Thesis, Osaka University (1985).
6. See e.g., A.G. Khachaturyan and G.A. Shatalov, Zh. Eksp. Teor. Fiz. 56 (1969) 1037 [Sov. Phys. JETP 29 (1969) 557].
7. See e.g., A.G. Khachaturyan and G.A. Shatalov, Zh. Eksp. Teor. Fiz. 56 (1969) 1037 [Sov. Phys. JETP 29 (1969) 557].
8. J. Ball and R.D. James, Arch. Rat. Mech. Anal. 100 (1987) 13; Phil. Trans. Roy. Soc. London A 338 (1992) 389.
9. J. Ball and R.D. James, Arch. Rat. Mech. Anal. 100 (1987) 13; Phil. Trans. Roy. Soc. London A 338 (1992) 389.
10. W.S. Wechsler, D.S. Lieberman and T.A. Read, Trans. AIME 197 (1953) 1503.
11. G.R. Barsch, B. Horovitz and J.A. Krumhansl, Phys. Rev. Lett. 59 (1987) 1251; B. Horovitz, G.R. Barsch and J.A. Krumhansl, Phys. Rev. B 43 (1991) 1021.
12. G.R. Barsch, B. Horovitz and J.A. Krumhansl, Phys. Rev. Lett. 59 (1987) 1251; B. Horovitz, G.R. Barsch and J.A. Krumhansl, Phys. Rev. B 43 (1991) 1021.
13. Z.S. Basinski and J.W. Christian, Acta Metall. 2 (1954) 148.
14. K. Shimizu and K. Otsuka, in: Shape Memory Effect in Alloys, ed. J. Perkins (Plenum, New York, 1975) p. 59; S. Ichinose, Y. Funatsu and K. Otsuka, Acta Metall. Mater. 33 (1985) 1613.
15. K. Shimizu and K. Otsuka, in: Shape Memory Effect in Alloys, ed. J. Perkins (Plenum, New York, 1975) p. 59; S. Ichinose, Y. Funatsu and K. Otsuka, Acta Metall. Mater. 33 (1985) 1613.
16. C. Chu, Ph.D. Thesis, Univ. Minnesota (1993); R. Abeyaratne, C. Chu and R.D. James, Phil. Mag. A 73 (1996) 457.
17. C. Chu, Ph.D. Thesis, Univ. Minnesota (1993); R. Abeyaratne, C. Chu and R.D. James, Phil. Mag. A 73 (1996) 457.
18. R.D. James, R.V. Kohn and T.W. Shield, J. Physique (Suppl.) 5 (1995) C8-253.
19. H.D. Chopra, A.L. Roytburd and M. Wuttig, Metall. Mater. Trans. 27A (1996) 1695.
20. E.M. Lifshitz, J. Phys. 8 (1994) 337.
21. J. Kaczér, Sov. Phys. JETP 19 (1964) 1204.
22. A. Hubert, Phys. Stat. Solidi 24 (1967) 669.
23. V.I. Marchenko, Sov. Phys. JETP 63 (1986) 1315.
24. I. Privorotskii, Thermodynamic Theory of Domain Structures (Wiley, New York, 1976).
25. M. Doi and T. Miyazaki, Phil. Mag. B 68 (1993) 305.
26. E.K.H. Salje, Phase Transitions in Ferroelastic and Co-elastic Crystals (Cambridge University Press, Cambridge, 1990).
27. R.V. Kohn and S. Müller, Phil. Mag. A 66 (1992) 697.
28. W.W. Schmahl et al., Phil. Mag. Lett. 60 (1989) 241; Y. Zhu, M. Suenaga and A.R. Moodenbaugh, Ultramicroscopy 37 (1991) 341.
29. W.W. Schmahl et al., Phil. Mag. Lett. 60 (1989) 241; Y. Zhu, M. Suenaga and A.R. Moodenbaugh, Ultramicroscopy 37 (1991) 341.
30. D. Fan and L.-Q. Chen, J. Am. Ceram. Soc. 78 (1995) 769.
31. See e.g. R.D. James and D. Kinderlehrer, Phil. Mag. B 68 (1993) 237.
32. G.R. Barsch and J.A. Krumhansl, Phys. Rev. Lett. 53 (1984) 1069; Metallurg. Trans. A 19 (1988) 761, p. 53; Proc. Int. Conf. on Martensitic Transformations (ICOMAT-92), eds. C.M. Wayman and J. Perkins (Monterey Institute of Advanced Studies, CA, 1993).
33. G.R. Barsch and J.A. Krumhansl, Phys. Rev. Lett. 53 (1984) 1069; Metallurg. Trans. A 19 (1988) 761, p. 53; Proc. Int. Conf. on Martensitic Transformations (ICOMAT-92), eds. C.M. Wayman and J. Perkins (Monterey Institute of Advanced Studies, CA, 1993).
34. G.R. Barsch and J.A. Krumhansl, Phys. Rev. Lett. 53 (1984) 1069; Metallurg. Trans. A 19 (1988) 761, p. 53; Proc. Int. Conf. on Martensitic Transformations (ICOMAT-92), eds. C.M. Wayman and J. Perkins (Monterey Institute of Advanced Studies, CA, 1993).
35. S. Kartha, T. Kastàn, J.A. Krumhansl and J.P. Sethna, Phys. Rev. Lett. 67 (1991) 3630; J.P. Sethna, S. Kartha, T. Kastàn and J.A. Krumhansl, Phys. Scripta T 42 (1992) 214; S. Kartha, J.A. Krumhansl, J.P. Sethna and L.K. Wickham, Phys. Rev. B 52 (1995) 803.
36. S. Kartha, T. Kastàn, J.A. Krumhansl and J.P. Sethna, Phys. Rev. Lett. 67 (1991) 3630; J.P. Sethna, S. Kartha, T. Kastàn and J.A. Krumhansl, Phys. Scripta T 42 (1992) 214; S. Kartha, J.A. Krumhansl, J.P. Sethna and L.K. Wickham, Phys. Rev. B 52 (1995) 803.
37. S. Kartha, T. Kastàn, J.A. Krumhansl and J.P. Sethna, Phys. Rev. Lett. 67 (1991) 3630; J.P. Sethna, S. Kartha, T. Kastàn and J.A. Krumhansl, Phys. Scripta T 42 (1992) 214; S. Kartha, J.A. Krumhansl, J.P. Sethna and L.K. Wickham, Phys. Rev. B 52 (1995) 803.
38. S. Semenovskaya and A.G. Khachaturyan, Phys. Rev. Lett. 67 (1991) 2223; Physica D 66 (1993) 205; S. Semenovskaya, Y. Zhu, M. Suenaga and A.G. Khachaturyan, Phys. Rev. B 47 (1993) 12 182.
39. S. Semenovskaya and A.G. Khachaturyan, Phys. Rev. Lett. 67 (1991) 2223; Physica D 66 (1993) 205; S. Semenovskaya, Y. Zhu, M. Suenaga and A.G. Khachaturyan, Phys. Rev. B 47 (1993) 12 182.
40. S. Semenovskaya and A.G. Khachaturyan, Phys. Rev. Lett. 67 (1991) 2223; Physica D 66 (1993) 205; S. Semenovskaya, Y. Zhu, M. Suenaga and A.G. Khachaturyan, Phys. Rev. B 47 (1993) 12 182.
41. A.M. Bratkovsky, E.K.H. Salje and V. Heine, Phase Trans. 52 (1994) 77; ibid. 55 (1995) 79.
42. A.M. Bratkovsky, E.K.H. Salje and V. Heine, Phase Trans. 52 (1994) 77; ibid. 55 (1995) 79.
43. A. Saxena, S.R. Shenoy, A.R. Bishop, Y. Wu and T. Lookman, J. Physique (Suppl.) 5 (1995) C8-125.
44. P.C. Clapp, Physica D 66 (1993) 26; in: Phase Transformations '87. ed. G.W. Lorimer (Inst. of Metals, London, 1988) p. 391.
45. P.C. Clapp, Physica D 66 (1993) 26; in: Phase Transformations '87. ed. G.W. Lorimer (Inst. of Metals, London, 1988) p. 391.
46. E.A.H. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944) p. 49.
47. See e.g. C.C. Chow and T. Hwa, Physica D 84 (1995) 494.
48. P.C. Hohenberg and B.I. Halperin, Rev. Mod. Phys. 49 (1977) 435.
49. C. Roland and R.C. Desai, Phys. Rev. B 42 (1990) 6658; C. Sagui and R.C. Desai, Phys. Rev. E 49 (1994) 2225; C. Sagui et al., A.M. Somoza and R.C. Desai, Phys. Rev. E 50 (1994) 4865.
50. C. Roland and R.C. Desai, Phys. Rev. B 42 (1990) 6658; C. Sagui and R.C. Desai, Phys. Rev. E 49 (1994) 2225; C. Sagui et al., A.M. Somoza and R.C. Desai, Phys. Rev. E 50 (1994) 4865.
51. C. Roland and R.C. Desai, Phys. Rev. B 42 (1990) 6658; C. Sagui and R.C. Desai, Phys. Rev. E 49 (1994) 2225; C. Sagui et al., A.M. Somoza and R.C. Desai, Phys. Rev. E 50 (1994) 4865.
52. L.-Q. Chen and A.G. Khachaturyan, Phys. Rev. Lett. 70 (1993) 1477.
53. J. Perkins, ed., Shape Memory Effect in Alloys (Plenum, New York, 1975).
54. B.A. Huberman and M. Kerszberg, J. Phys. A: Math. Gen. 18 (1985) L331; D. Kumar and S.R. Shenoy, Solid State Commun. 57 (1986) 927.
55. B.A. Huberman and M. Kerszberg, J. Phys. A: Math. Gen. 18 (1985) L331; D. Kumar and S.R. Shenoy, Solid State Commun. 57 (1986) 927.
56. See e.g. Proc. Int. Conf. on Martensitic Transformations (ICOMAT-95), eds. R. Gotthardt and J. Van Humbeeck (Lausanne, Switzerland, 1995) [J. Physique (Suppl.) Colloque 8 (1995) 5].
57. See e.g. Proc. Int. Conf. on Martensitic Transformations (ICOMAT-95), eds. R. Gotthardt and J. Van Humbeeck (Lausanne, Switzerland, 1995) [J. Physique (Suppl.) Colloque 8 (1995) 5].