 | | 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
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| D. L. Bykov and D. N. Konovalov, "Nonlinear endochronous theory of aging viscoelastic materials," Mech. Solids. 37 (4), 52-62 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
4 |
Pages |
52-62 |
| Title |
Nonlinear endochronous theory of aging viscoelastic materials |
| Author(s) |
D. L. Bykov (Korolev)
D. N. Konovalov (Korolev) |
| Abstract |
We consider a generalization of the nonlinear
theory of viscoelasticity to allow for the aging
processes of both mechanical and non-mechanical nature.
A distinguishing feature of this theory, as compared with
other nonlinear versions of the theory of viscoelasticity,
is that it utilizes Maxwell's mechanical model with
characteristics depending on the parameters accounting for
various processes of loading, unloading, deformation,
and cumulative damage of materials. Utilizing a large number
of such elementary models allows one to approximate
the relaxation kernels by the sum of exponential functions
with any degree of accuracy. The dependence of the viscosity
coefficients in Maxwell's models on the aforementioned
parameters leads to an endochronous theory of viscoelasticity,
whereas a similar dependence of elastic characteristics of these
models changes purely endochronous nature of the theory
thereby allowing one to take into account the material aging.
This is just the approach that is adopted in the present paper.
A number of issues associated with the identification
of the material functions of the proposed theory are considered.
Utilizing Maxwell's model as the basis one allows one to analyze
the structure of the specific work of internal forces for any
parameters of nonlinearity. An essential point is representing
the specific work of internal forces as the sum of separate
components each of which has a clear physical meaning, namely,
instantaneous reversible elastic energy, delayed reversible
elastic energy, dissipated energy, mechanical and chemical aging
energies, and the specific work of stresses on the thermal
strains of the material. All these components can be utilized
to describe various processes in aging viscoelastic materials.
A version of the kinetic equation is proposed for the specific
dissipated energy that is the dissipated energy portion
associated with structural changes (cumulative damage)
in the material. A long-term strength criterion is formulated
in terms of the specific absorbed energy. The application
of this criterion to the process of two-stage creep of a filled
polymer material allows one to account for specific features
of changes in the residual durability of the material that are observed
in experiments. |
| References |
| 1. | A. A. Il'yushin and B. E. Pobedrya, Fundamentals of the Mathematical
Theory of Thermoviscoelasticity [in Russian], Nauka, Moscow, 1970. |
| 2. | D. L. Bykov, "On accounting for damage in filled polymer materials,"
Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 19-28, 1998. |
| 3. | D. L. Bykov, "Modelling damage accumulation in filled polymers,"
Fatigue and Fracture of Engineering Materials and Structures, Vol. 22, No. 11,
pp. 981-988, 1999. |
| 4. | D. L. Bykov and D. N. Konovalov, "Identification of the material
functions in a nonlinear theory of thermoviscoelasticity taking into account
there hierarchical structure,"
Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 189-205, 1999. |
| 5. | V. V. Moskvitin, Strength of Viscoelastic Materials
[in Russian], Nauka, Moscow, 1972. |
| 6. | Yu. S. Urzhumtsev, Prediction of Long-term Strength
in Polymer Materials [in Russian], Nauka, Moscow, 1982. |
| 7. | D. L. Bykov and D. N. Konovalov, "Specific features
of strength of viscoelastic materials during buckling
of thin-walled structures," in Physics of Deformation and Damage
Processes and Prediction of Mechanical Behavior of Materials.
Proceedings of the International Seminar "Topical Problems
of Strength." Part 2 [in Russian], pp. 428-433, Vitebskii Gos.
Tekhnnol. Un-t, Vitebsk, 2000. |
| 8. | D. L. Bykov and D. N. Konovalov, "Utilizing
the dissipated energy function to describe deformation and damage
of polymer structures," in Elasticity and Non-elasticity.
Materials of the International Symposium on Problems of Mechanics
of Solids Devoted to 90th Birthday Anniversary
of A. A. Il'yushin [in Russian], pp. 250-262, Izd-vo MGU, Moscow, 2001. |
| 9. | J. P. Carden, "An investigation of the applicability
of a damage failure theory for solid rocket propellants,"
AIAA Paper, No. 92-0132, pp. 1-6, 1992. |
|
| Received |
12 February 2002 |
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