Multi-cell continuum approximation for discrete medium with microscopic rotations

Physica Status Solidi (B) Basic Research

Volumn 242, Issue 3, 2005, Pages 528-537

  Dmitriev, S V ^a,b   Vasiliev, A A ^c   Yoshikawa, N ^a   Shigenari, T ^d   Ishibashi, Y ^e  

^a INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

^b NATIONAL INSTITUTE FOR MATERIALS SCIENCE   (Japan)

^c TVER STATE UNIVERSITY   (Russian Federation)

^d UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

^e AICHI SHUKUTOKU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 15344338944     PISSN: 03701972     EISSN: None     Source Type: Journal    
DOI: 10.1002/pssb.200460373     Document Type: Article

References (51)

1. E. C. Aifantis, Mech. Mater. 35, 259 (2003).
2. E. Cosserat and F. Cosserat, Theorie des Corps Deformables (A. Hermann et Fils, Paris, 1909).
3. A. C. Eringen, Microcontinuum Field Theories: Foundations and Solids (Springer-Verlag, New York 1999).
4. G. A. Maugin, Nonlinear Waves in Elastic Crystals (Oxford University Press, Oxford 1999).
5. R. Blinc and A. P. Levanyuk (eds.), Incommensurate Phases in Dielectrics (North Holland, Amsterdam, 1986).
6. S. A. Wells, M. T. Dove, M. G. Tucker, and K. Trachenko, J. Phys.: Condens. Matter 14, 4645 (2002).
7. M. Vallade, B. Berge, and G. Dolino, J. Phys. 12, 1481 (1992).
8. S. V. Dmitriev, D. A. Semagin, T. Shigenari, K. Abe, M. Nagamine, and T. A. Aslanyan, Phys. Rev. B 68, 052 101. (2003)
9. H. Kimizuka, H. Kaburaki, and Y. Kogure, Phys. Rev. Lett. 84, 5548 (2000).
10. M. B. Smirnov and A. P. Mirgorodsky, Phys. Rev. Lett. 78, 2413 (1993).
11. N. R. Keskar and J. R. Chelikowsky, Phys. Rev. B 48, 16 227 (1993).
12. A. Alderson and K. E. Evans, Phys. Rev. Lett. 89, 225 503 (2002).
13. M. B. Smirnov, Phys. Rev. B 59, 4036 (1999).
14. M. T. Dove et al., Phys. Rev. Lett. 78, 1070 (1997). I. P. Swainson and M. T. Dove, Phys. Rev. Lett. 71, 193 (1993).
15. M. T. Dove et al., Phys. Rev. Lett. 78, 1070 (1997). I. P. Swainson and M. T. Dove, Phys. Rev. Lett. 71, 193 (1993).
16. K. W. Wojciechowski, Phys. Lett. A 137, 60 (1989).
17. Y. Ishibashi and M. Iwata, J. Phys. Soc. Jpn. 69, 2702 (2000).
18. J. N. Grima and K. E. Evans, J. Mater. Sci. Lett. 19, 1563 (2000).
19. K. W. Wojciechowski, J. Phys. A, Math. Gen. 36, 11765 (2003).
20. D. A. Konyok, K. W. Wojciechowski, Yu. M. Pleskatchevskii, and S. V. Shilko, Mechanics of Composite Materials Structures Moscow, in press (in Russian).
21. K. W. Wojciechowski, K. V. Tretiakov, and M. Kowalik, Phys. Rev. E 67, 036 121 (2003).
22. K. W. Wojciechowski, in: AIP Conference Proceedings, Vol. 708, edited by M. Tokuyama and I. Oppenheim, Third International Symposium on Slow Dynamics in Complex Systems, Sendai (Japan, November 2003), in press. K. W. Wojciechowski, in: Properties and Applications of Nanocrystalline Alloys from Amorphous Precursor, edited by B. Idzikowski, P. Švec, and M. Miglierini (Kluwer Academic Publishers, Dordrecht, 2004).
23. K. W. Wojciechowski, in: AIP Conference Proceedings, Vol. 708, edited by M. Tokuyama and I. Oppenheim, Third International Symposium on Slow Dynamics in Complex Systems, Sendai (Japan, November 2003), in press. K. W. Wojciechowski, in: Properties and Applications of Nanocrystalline Alloys from Amorphous Precursor, edited by B. Idzikowski, P. Švec, and M. Miglierini (Kluwer Academic Publishers, Dordrecht, 2004).
24. A. Vasiliev, S. V. Dmitriev, Y. Ishibashi, and T. Shigenari, Phys. Rev. B 65,094101 (2002).
25. S. V. Dmitriev, T. Shigenari, A. A. Vasiliev, and K. Abe, Phys. Rev. B 55, 8155 (1997).
26. S. V. Dmitriev, T. Shigenari, and K. Abe, Phys. Rev. B 58, 2513 (1998). S. V. Dmitriev, Phys. Solid State 45, 352 (2003).
27. S. V. Dmitriev, T. Shigenari, and K. Abe, Phys. Rev. B 58, 2513 (1998). S. V. Dmitriev, Phys. Solid State 45, 352 (2003).
28. S. V. Dmitriev, A. A. Vasiliev, and N. Yoshikawa, Recent Res. Devel. Physics 4, 267 (2003).
29. O. M. Braun, and Y. S. Kivshar, The Frenkel-Kontorova model: concepts, methods and applications (Springer, Berlin, 2004).
30. J. J. M. Slot and T. Janssen, Physica D 32, 27 (1988).
31. Y. Ishibashi, J. Phys. Soc. Jpn. 60, 212 (1991).
32. J. Hlinka, H. Orihara, and Y. Ishibashi, J. Phys. Soc. Jpn. 67, 3488 (1998).
33. S. V. Dmitriev, K. Abe, and T. Shigenari, Ferroelectrics 237, 17 (2000).
34. E. A. Il'iushina, Prikl. Mat. Mekh. 36, 1019 (1972); ibid 33, 896 (1969).
35. E. A. Il'iushina, Prikl. Mat. Mekh. 36, 1019 (1972); ibid 33, 896 (1969).
36. A. Vasiliev, Mosc. Univ. Mech. Bull. 51, 44 (1996); ibid 49, 71 (1994).
37. A. Vasiliev, Mosc. Univ. Mech. Bull. 51, 44 (1996); ibid 49, 71 (1994).
38. S. V. Dmitriev, T. Shigenari, and K. Abe, J. Phys. Soc. Jpn. 66, 2732 (1997).
39. S. V. Dmitriev, K. Abe, and T. Shigenari, J. Phys. Soc. Jpn. 65, 3938 (1996).
40. S. V. Dmitriev, K. Abe, and T. Shigenari, Physica D 147, 122 (2000).
41. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon Press, Oxford, 1986).
42. U. Scharer and P. Wachter, Mater. Sci. Forum 210-213, 811 (1996). U. Scharer and P. Wachter, Solid State Commun. 96, 497 (1995).
43. U. Scharer and P. Wachter, Mater. Sci. Forum 210-213, 811 (1996). U. Scharer and P. Wachter, Solid State Commun. 96, 497 (1995).
44. S. V. Dmitriev, T. Shigenari, and K. Abe, J. Phys. Soc. Jpn. 70, 1431 (2001).
45. K. W. Wojciechowski, J. Phys. Soc. Jpn. 72, 1820 (2003).
46. R. S. Lakes, Science 288, 1976 (2000).
47. B. M. Lempriere, AIAA Journal 6, 2226 (1968).
48. D. J. Gunton and G. A. Saunders, J. Mater. Sci. 7, 1061 (1972).
49. R. H. Baughman, J. M. Shacklette, A. A. Zakhidov, and S. Stafstrom, Nature 392, 362 (1998).
50. R. S. Lakes, Trans. of ASME 115, 696 (1993). C. W. Smith, J. N. Grima, and K. E. Evans, Acta Mater. 48, 4349 (2000).
51. R. S. Lakes, Trans. of ASME 115, 696 (1993). C. W. Smith, J. N. Grima, and K. E. Evans, Acta Mater. 48, 4349 (2000).