 | | 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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| << Previous article | Volume 41, Issue 6 / 2006 | Next article >> |
| D. L. Bykov and D. N. Konovalov, "Endochronic model of mechanical behavior of ageing viscoelastic materials at finite strains," Mech. Solids. 41 (6), 110-120 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
6 |
Pages |
110-120 |
| Title |
Endochronic model of mechanical behavior of ageing viscoelastic materials at finite strains |
| Author(s) |
D. L. Bykov (Korolev)
D. N. Konovalov (Korolev) |
| Abstract |
We consider a generalization of the nonlinear endochronic theory of ageing
viscoelastic materials [1] to the case of finite strains. Our
generalization preserves the main advantages of the model proposed earlier
in [1]. Namely, it has a unique apparatus for describing the influence of
the basic physical-mechanical factors (such as temperature, humidity,
chemical ageing, strain and stress level, sign of the average stress, sign
of the strain and loading rate, etc.) and provides a possibility of
performing a structure-energy analysis of the stress-strain state [2-4].
The model is described by a system of relations of incremental type. These
relations are derived in the following three stages. At the first stage, it
is assumed that the principal directions of the true stress tensor are
"frozen" in the material of the particle and three scalar constraints of
hereditary type between the principal true stresses and logarithmic strains
are stated. The form of these relations is similar to the form of relations
in the endochronic theory [1]. At the second stage, the scalar relations of
incremental type are derived on the basis of the assumption that the
logarithmic strain rates, as well as the rates of variation of the reduced
times, are constant on the interval [t,t+Δt]. At the third stage,
the incremental relations are stated in tensor form and generalized to the
case of an arbitrary history of material particle deformation.
We consider an algorithm for numerically solving 3D initial boundary-value
problems for the proposed system of incremental constitutive relations. The
algorithm is based on a FEM discretization of the weak form of the
equilibrium equations referred to the body configuration at the beginning
of the current time step. The dependence of the material ageing functions
and the functions of the rates of reduced times on state parameters
(strain invariants, stresses, specific scattered energy, etc.) is taken
into account in the framework of the explicit scheme.
We solve the problem of constrained compression of a rubber shock-absorber
using the above algorithm. The material constants of the model were
identified according to the results of experiments on uniaxial relaxation
of compressive stresses. We note that for small values of the edge radius
of the rim through which the compressive force is applied to the rubber
disk, there is a sharp decrease in the convergence rate of the Newton
method used to solve the system of nonlinear equations for the increments
of the nodal displacements. We propose an extrapolation (in the value of
the edge radius) computation procedure. Comparison with the results of
experiments on constrained compression of a shock-absorber shows a
satisfactory correspondence between the numerical and experimental results. |
| References |
| 1. | D. L. Bykov and D. N. Konovalov, "Nonlinear endochronic theory of
ageing viscoelastic materials," Izv. RAN. MTT [Mechanics of Solids],
No. 4, pp. 63-76, 2002. |
| 2. | D. L. Bykov, "Use of the structural components of the specific
work of internal forces to describe the resistance of viscoelastic
materials," Izv. RAN. MTT [Mechanics of Solids], No. 3, pp. 99-111, 2003. |
| 3. | V. E. Apet'yan and D. L. Bykov, "Structure-energy analysis of
uniaxial stress-strain state under compression and unloading of
viscoelastic materials," Izv. RAN. MTT [Mechanics of Solids], No. 6,
pp. 63-76, 2005. |
| 4. | D. L. Bykov, "Method of structure-energy analysis of stress-strain
state of viscoelastic materials," Vestnik MGU, Ser. 1, Mathematics,
Mechanics, No. 1, pp. 59-62, 2006. |
| 5. | A. A. Il'yushin and B. E. Pobedrya,
Foundations of Mathematical Theory of Thermoviscoelasticity [in Russian],
Nauka, Moscow, 1970. |
| 6. | F. J. Lockett,
Nonlinear Viscoelastic Solids, Acad. Press, New York, 1972. |
| 7. | R. I. Tanner,
"From A to (BK)Z in constitutive relations,"
J. Rheology, Vol. 32, No. 7, pp. 673-702, 1988. |
| 8. | L. M. Yang, V. P. W. Shim, and C. T. Lim,
"A visco-hyperelastic approach to modelling the constitutive
behavior of rubber,"
Intern. J. Impact Engineering, Vol. 24, pp. 545-560, 2000. |
| 9. | D. L. Bykov and D. N. Konovalov,
"Determining material functions in the nonlinear theory of thermoviscosity
with the use of its hierarchic structure,"
Izv. RAN. MTT [Mechanics of Solids], No. 5, pp. 189-205, 1999. |
| 10. | D. L. Bykov and D. N. Konovalov,
"Computational estimate of the influence of damaged fuels
on the strength of the rocket engine charges made of these fuels,"
Raketostroenie i Kosmonavtika, No. 16, pp. 82-91, 1999. |
| 11. | K. Trusdell, A First Course of Rational Continuum Mechanics [Russian translation],
Mir, Moscow, 1975. |
| 12. | O. Zienkiewicz,
Finite Element Method in Technology [Russian translation],
Mir, Moscow, 1975. |
| 13. | D. L. Bykov and V. A. Shachnev,
"On a generalization of elastic solution method,"
PMM [Applied Mathematics and Mechanics], Vol. 33, No. 2,
pp. 290-298, 1969. |
|
| Received |
02 June 2006 |
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