 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
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| K. V. Kukudzhanov, "A two-velocity model of elasto-visco-plastic deformation of composite materials," Mech. Solids. 36 (5), 56-66 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
5 |
Pages |
56-66 |
| Title |
A two-velocity model of elasto-visco-plastic deformation of composite materials |
| Author(s) |
K. V. Kukudzhanov (Moscow) |
| Abstract |
A model representing an inhomogeneous composite material as
a homogeneous anisotropic elasto-visco-plastic medium was proposed in [1].
That model was used for solving some nonstationary problems of dynamic
deformation and fracture of inelastic laminated composite bodies.
This approach yields fairly good averaged characteristics of the
stress-strain state, but it does not describe the local effects
related to the heterogeneous structure of the composite, although
these effects may be considerable, especially in dynamical problems.
In this connection, a number of attempts [2-7] were undertaken
to examine these effects in elastic as well as inelastic composites.
In the present paper, multi-velocity models of continuous media
are used to model a two-phase composite material consisting of
elastic fibres or layers supported by an inelastic
viscoplastic matrix. We obtain a complete system of
dynamical equations which take into account the
elasto-visco-plastic interaction of the matrix and the fibers.
This system is used in the second part of the paper for the
investigation of the differences between one- and two-velocity
models. The results obtained are compared with experimental data,
which confirms the advantage of this approach. |
| References |
| 1. | K. V. Kukudzhanov, "Dynamic deformation and fracture of inelastic
laminated composites," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 4, pp. 87-98, 1977. |
| 2. | A. Bedford and M. Stern, "Multi continuum theory for composite
elastic materials," Acta Mech., Vol. 14, No. 2/3, pp. 85-102, 1972. |
| 3. | S. E. Martin, A. Bedford, and M. Stern,
"Steady state wave propagation in fibre-reinforced elastic materials,"
in Development in Mech. Proc. 12th Midwestern Conf.,
Vol. 6, pp. 512-527, Notre Dam, 1971. |
| 4. | G. A. Hegemier, "Finite-amplitude elastic plastic wave propagation
in laminated composites,"
J. Appl. Phys., Vol. 45, pp. 4248-4253, 1974. |
| 5. | H. D. McNiven and Y. Mengi, "A mathematical model for the linear
dynamic behavior of two-phase
periodic materials," Intern. J. Solids and Structures,
Vol. 15, No. 4, pp. 271-280, 1979. |
| 6. | M. Stern and A. Bedford, "Wave propagation in elastic laminates
using multicontinuum theory," Acta Mech., Vol. 15, No. 1/2, pp. 21-38,
1972. |
| 7. | L. P. Khoroshun, "On the theory of interpenetrating elastic
mixtures,", Prikl. Mekhanika, Vol. 13, No. 10, pp. 124-132, 1979. |
| 8. | A. E. Green and P. M. Naghdi, "On basic equations of mixtures,"
Quart. J. Mech. Appl. Math., Vol. 22, No. 4, pp. 427-438, 1969. |
| 9. | R. I. Nigmatullin, Dynamics of Multi-Phase Media. Part. 1[in Russian],
Nauka, Moscow, 1987. |
| 10. | M. A. Biot, "Theory of propagation of elastic waves in a fluid
saturated porous solid," J. Acoust. Soc. Amer., Vol. 28, No. 2, pp.
168-191, 1956. |
| 11. | A. J. M. Spencer (Editor), Continuum Theory of the Mechanics of
Fiber-Reinforced Composites, Springer-Verlag, New York, 1984. |
| 12. | V. N. Kukudzhanov, "Numerical simulation of dynamic deformation and fracture
of elastic-plastic media," Uspekhi Mekhaniki [Advances in Mechanics],
Vol. 8, No. 4, pp. 21-65, 1985. |
|
| Received |
06 October 1999 |
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