The concept of multifractal elasticity

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 210, Issue 1-2, 1996, Pages 51-59

  Balankin, Alexander S ^a,b  

^a Dzerzhinski Military Academy   (Russian Federation)

^b SCHOOL OF ENGINEERING AND SCIENCES   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTITUTIVE EQUATIONS; ELASTICITY; MICROSTRUCTURE;

CLOSED SYSTEMS; CORRELATION DIMENSIONS; ELASTIC BEHAVIOR; MECHANICAL BEHAVIOR OF MATERIALS; MULTI FRACTALS; MULTIFRACTAL STRUCTURE; RANDOM MICROSTRUCTURE; REVERSIBLE DEFORMATION;

FRACTALS;

EID: 0009145585     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/0375-9601(95)00874-8     Document Type: Article

References (51)

1. S. Torquato, Appl. Mech. Rev. 44 (1991) 37.
2. D. Jeulin, in: Advances in mathematical modeling of composite materials, ed. K.Z. Markov (World Scientific, Singapore, 1994) p. 239.
3. A.S. Balankin and P. Tamayo, Rev. Mex. Fís. 40 (1994) 506.
4. V.S. Ivanova, A.S. Balankin, I. Bunin and A. Oksogoev, Synergetics and fractals in material science (Nauka, Moscow, 1994).
5. J. Feder, Fractals (Freeman, New York, 1988).
6. J.M. Perdang, in: Applying fractals in astronomy, eds. A. Neck and J.M. Perdang (Springer, Berlin, 1991) p. 1.
7. A.S. Balankin, Synergetics of deformed solid (Department of Defense of the USSR Press, Moscow, 1992).
8. A.S. Balankin, Sov. Phys. Solid State 34 (1992) 889.
9. B.H. Lavenda and A. Florio, Int. J. Theor. Phys. 31 (1992) 1455.
10. P. Grassberger and P. Procaccia, Phys. Rev. Lett. 50 (1983) 346; Physica D 9 (1983) 189
11. P. Grassberger and P. Procaccia, Phys. Rev. Lett. 50 (1983) 346; Physica D 9 (1983) 189
12. A.S. Balankin, Dokl. Akad. Nauk SSSR 319 (1991) 1098.
13. A.S. Balankin, Sov. Phys. Dokl. 37 (1992) 379.
14. B.B. Mandelbrot, The fractal geometry of nature (Freeman, San Francisco, 1982).
15. I.A. Kunin, Elastic media with microstructure (Springer, Berlin, 1982).
16. D.J. Bergman and Y. Kantor, Phys. Rev. Lett. 53 (1984) 511.
17. E. Duering and D.J. Bergman, Phys. Rev. B 37 (1988) 9460.
18. I. Webman, in: Fractals in physics, eds. L. Pietronero and E. Tosatti (Elsevier, Amsterdam, 1986) p. 343.
19. Y. Kantor, Physica D 38 (1989) 215.
20. R.C. Ball, Physica D 38 (1989) 13.
21. A.S. Balankin, Sov. Tech. Phys. Lett. 17 (1991) 632.
22. A.S. Balankin and A.L. Bugrimov, Polymer Sci. 34 (1992) 889.
23. A.S. Balankin and A.L. Bugrimov, in: Abstracts XXVIII Int. Congr. on Theoretical and applied mechanics, Haifa, Israel, 22-28 August 1992 (Int. Union Theor. and Appl. Mech. Press, Haifa, 1992) p. 17.
24. T.A. Vilgis, in: Synthesis, characterisation, and theory of polymer networks and gels. ed. S.M. Aharoni (Plenum, New York, 1992) p. 13.
25. G. Heinring and T.A. Vilgis, Europhys. Lett. 25 (1994) 175
26. R.W. Hertzberg, Deformation and fracture mechanics of engineering materials (Wiley, New York, 1989).
27. L.D. Landau and E.M. Lifshitz, Theor of elasticity (Pergamon, New York, 1970).
28. E. Kröner, in: Modelling small deformations of polycrystals, eds. J. Gittus and J. Zarka (Elsevier, Amsterdam, 1986) p. 229.
29. L. Treloar, The physics of rubber elasticity (Clarendon, Oxford, 1975).
30. H.M. James and E. Guth. J. Chem. Phys. 11 (1943) 455.
31. P.J. Flory and J. Rehner, J. Chem. Phys. 11 (1943) 512.
32. F.T. Wall, J. Chem. Phys. 11 (1943) 527.
33. L. Treloar, Trans. Faraday Soc. 39 (1943) 36.
34. Yu. Zuev, B.M. Kaporovskii and N.N. Yurtsev, Phys. Dokl. 39 (1994) 388.
35. E.A. Frils, R.S. Lakes and J.B. Park. J. Mater. Sci. 23 (1988) 4406.
36. P. Pincus, Macromolecules 9 (1976) 386.
37. P.G. de Gennes, Scaling concepts in polymer physics (Cornell Univ. Press, Ithaca, 1979).
38. A.K. Mal and S.J. Singh, Deformation of elastic solids (Prentice-Hall, Englewood Cliffs, NJ, 1991).
39. A.S. Balankin, Elastic behavior of materials with multifractal structure, Phys. Rev. B (1996), to be published.
40. G.P. Cherepanov, Mechanics of composite materials (Nauka, Moscow, 1983).
41. A.S. Balankin, Sov. Tech. Phys. Lett. 17 (1991) 229, 391.
42. M.B. Isichenko, Rev. Mod. Phys. 64 (1992) 961.
43. B.M. Smirnov, Physics of fractal clusters (Nauka, Moscow, 1991).
44. S.M. Aharoni, in: Synthesis, characterisation, and theory of polymer networks and gels, ed. S.M. Aharoni (Plenum, New York, 1992) p. 1.
45. M. Kallala, C. Sanches and B. Cabane, Phys. Rev. E 48 (1993) 3692.
46. M. Gronauer, A. Kadur and J. Fricke, in: Proc. 1st Int. Symp. on Aerogels, Wurzburg, Germany. 1985 (Springer, Berlin, 1986).
47. S.P. Obukhov, M. Rubinstein and R.H. Colby, Macromolecules 27 (1994) 3191.
48. C.E. Puente, Phys. Lett. A 161 (1992) 441.
49. A. Bunde and Sh. Havlin, eds., Fractals in physics (Springer, Berlin, 1994).
50. S. Edwards and T. Vilgis, Rep. Prog. Phys. 51 (1988) 243.
51. M.H. Wagner, J. Rheol. 38 (1994) 655.