Self-consistent methods in the problem of axial elastic shear wave propagation through fiber composites

Archive of Applied Mechanics

Volumn 73, Issue 1-2, 2003, Pages 105-130

  Kanaun, S K ^a   Levin, V M ^b  

^a SCHOOL OF ENGINEERING AND SCIENCES   (Mexico)

^b INSTITUTO MEXICANO DEL PETRÓLEO   (Mexico)

Author keywords

Alternation factor; Dispersion; Fiber composite; Self consistent method; Shear wave

Indexed keywords

ATTENUATION; MICROSTRUCTURE; SHEAR WAVES; WAVE PROPAGATION;

FIBER COMPOSITES;

COMPOSITE MATERIALS;

EID: 0041363281     PISSN: 09391533     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00419-002-0250-9     Document Type: Article

References (32)

1. O'Connell, R.; Budiansky, B.: Seismic velocities in dry and saturated cracked solids. J Geophys Res 79 (1974) 5412-5426
2. Sabina, F.; Willis, J.: A simple self-consistent analysis of wave propagation in particulate composites. Wave Motion 10 (1988) 127-142
3. Sabina, F.; Willis, J.: Self-consistent analysis of waves in a polycrystalline medium. Eur J Mech A/Solids 12 (1993) 265-275
4. Kanaun, S.: Propagation of elastic waves through polycrystalline materials. Eur J Mech A/Solids 15 (1996) 859-881
5. Kanaun, S.: Propagation of scalar waves through matrix composite materials: effective medium approach. Eur J Mech A/Solids 16 (1997) 1041-1066
6. Foldy, L.: The multiple scattering of waves. Phys Rev 67 (1945) 107-119
7. Lax, M.: Multiple scattering of waves. Rev Modern Phys 23 (1951) 287-310
8. Lax, M.: Multiple scattering of waves II. The effective field in dense systems. Phys Rev 85 (1952) 621-629
9. Mal, K.; Knopoff, L.: Elastic wave velocities in two-component systems. J Inst Math Appl 3 (1967) 376-587
10. Bose, S.; Mal, A.: Longitudinal shear waves in a fiber reinforced composites. Int J Solids Struct 9 (1973) 1075-1085
11. Bose, S.; Mal, A.; Axial shear waves in a medium with randomly distributed cylinders. J Acoust Soc Am 55 (1974) 519-523
12. Datta, S.: Scattering by a random distribution of inclusion and effective elastic properties. Proc of the 2nd Int Symposium on Continuum Models of Discrete Systems, (1978) 111-127
13. Willis, J.: A polarization approach to the scattering of elastic waves I, II. J Mech Phys Solids 28 (1980) 287-327
14. Varadan, V.K.; Varadan, V.V.; Pao, Y.: Multiple scattering of elastic waves by cylinders of arbitrary cross sections. I. SH-waves. J Acoust Soc Am 63 (1978) 1310-1319
15. Varadan, V.K.; Varadan V.V.: A multiple scattering theory for elastic wave propagation in discrete random media. J Acoust Soc Am 77 (1985) 375-385
16. Datta, S.; Ledbetter, H.; Shindo, Y.; Shan, A.: Phase velocities and attenuation of plane waves in a particle-reinforced composite medium. Wave Motion 10 (1988) 171-182
17. Kanaun, S.; Levin, V.: Effective field method on the mechanics of matrix composite materials. Petrozavodsk: Petrozavodsk State University press, 1993
18. Kanaun, S.; Levin, V.: Effective field method on the mechanics of matrix composite materials. In: Markov, K. (ed.) Advances in Mathematical Modeling of Composite Materials, Series on Advances in Mathematics for Applied Sciences XV, pp. 1-58. Singapore, New Jersey, London, Hong Kong: World Scientific Publishing 1994
19. Budiansky, B.: On the elastic moduli of some heterogeneous materials. J Mech Phys Solids 13 (1965) 223-234
20. Hill, R.: Self-consistent mechanics of composite materials. J Mech Phys Solids 13 (1965) 213-222
21. Bruggeman, D.: Berechnung verschidener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen. Ann Phys 24 (1935) 636-679
22. Kanaun, S.: Effective field method in linear problems of statics of composite media. App Math Mech (PMM) 46 (1982) 655-665
23. Kanaun, S.: Elastic medium with random fields of inhomogeneities. In: Kunin, I. Elastic Media with Microstructure II, Springer Series in Solid-State Sciences 44, pp. 165-228. Berlin, Heidelberg, New York: Springer 1983
24. Bringen, A.; Suhubi, E.: Elastodynamics II. New York: Academic Press 1975
25. Bohren, C.; Huffman, D.: Absorption and Scattering of Light by Small Particles. New York: John Wiley & Sons 1983
26. Talbot, D.; Willis, J.: Variational estimates for dispersion and attenuation of waves in random composites-III, Fiber-reinforced materials. Int J Solids Struct 19 (1983) 793-811
27. Torquato, S.: Exact conditions on physically realizable correlation functions of random media. J Chem Phys 111 (1999) 8832-8837
28. Dean, G.; Lockett, F.: Determination of the mechanical properties of fiber composites by ultrasonic techniques. Am Soc Testing Mat STP, N521 (1973) 326-346
29. Ivanov, A.; Loyko, V.; Dick, V.: Propagation of Light in Dense Packed Dispersed Systems. Minsk: Nauka i Tehnika 1983
30. Kanaun, S.: Self-consistent methods in the problem of wave propagation through heterogeneous media. In: Markov, K., Preziosi, L. (eds) Heterogeneous Media. Micromechanical Modeling, Methods and Simulations, pp. 241-320. Boston, Basel, Berlin: Birkhauser 2000
31. Kerner, E.: The elastic and thermoelastic properties of composite media. Proc Phys Soc 69 (B) (1956) 801-813
32. Christensen, R.; Lo, L.: Solution for effective shear properties in three phase and cylinder models. J Mech Phys Solids 27 (1979) 315-330