 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| D. L. Bykov, "Utilization of structural components of specific work of internal forces for the description of strength of viscoelastic materials," Mech. Solids. 38 (3), 78-87 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
3 |
Pages |
78-87 |
| Title |
Utilization of structural components of specific work of internal forces for the description of strength of viscoelastic materials |
| Author(s) |
D. L. Bykov (Korolev) |
| Abstract |
The invariants of strain and stress tensors are widely
used in state equations which take into account physically
nonlinear material properties. These invariants do not depend
on mechanical characteristics, and this facilitates their
calculation but makes more difficult the description of
complex rheological properties of some materials,
for instance, polymers.
The utilization of formally time-reversible invariants
as arguments of material functions and functionals
characterizing reversible and irreversible processes of
deformation, damage accumulation, aging,
and healing increases the difficulty of finding
suitable functions and functionals.
As will be shown below, in many cases some other invariants
(apart from those mentioned above) can be used, namely,
one can use components of the specific work of internal forces.
Analysis of these components for various types
of loading and unloading allows us to evaluate
predictions made on the basis of some theories about
various experimentally observed physical
phenomena. Thus, the analysis of the structure of the specific work of
internal forces is useful for establishing a priori
estimates of the applicability range of any theory.
This idea is demonstrated by a nonlinear endochronous
theory of aging viscoelastic materials based on
the generalized Kelvin-Voigt model. Previously,
similar investigations were carried out for the generalized
nonlinear Maxwell model [1]. These models take into account
the nonlinearity of elastic and viscous properties of
materials and allow us to construct creep and relaxation curves
with any given accuracy. For each of these models,
the specific work is represented as the sum of five components,
each with its own physical meaning: instantaneously and
slowly reversible specific energies, specific scattered
energy, specific aging energy, and the specific work of
average stress on a volume deformation of free thermal expansion.
These components are invariants and contain mechanical
characteristics of materials. Their clear physical meaning
makes them convenient for being taken as arguments
of material functions and functionals. This is confirmed by
experiments mentioned in [1-5], where the generalized Maxwell
model is adopted as the theoretical basis. In the present paper,
a similar confirmation is given on the basis of the generalized
Kelvin-Voigt model, by means of theoretical analysis
of the experimental dependence of the sound speed on
the level of creep of a filled polymer
sample under loading and unloading. |
| References |
| 1. | D. L. Bykov and D. N. Konovalov,
"A nonlinear endochronous theory of aging viscoelastic materials,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 63-76, 2002. |
| 2. | D. L. Bykov and D. N. Konovalov,
"Determination of material functions in the nonlinear theory of
thermoviscoelasticity with the help of its hierarchical structure," Izv.
AN. MTT [Mechanics of Solids], No. 5, pp. 189-205, 1999. |
| 3. | D. L. Bykov and D. N. Konovalov,
"Some properties of strength of viscoelastic materials
in the case of buckling of thin-walled structures,"
in Proc. XXXVI Intern. Seminar "Modern Problems of Strength." Part 2,
pp. 428-433, Vitebsk. Gos. Tekhnol. Un-t, Vitebsk, 2000. |
| 4. | D. L. Bykov and D. N. Konovalov,
"Utilization of the scattered energy function for the description of
strains and fracture in polymer structures,"
in Elasticity and Inelasticity. Proc. Intern. Symp. on Mechanics of
Solids dedicated to A. A. Il'yushin, pp. 250-262, Izd-vo MGU, Moscow,
2001. |
| 5. | V. E. Apet'yan and D. L. Bykov,
"Determination of nonlinear viscoelastic characteristics
of filled polymer materials,"
Kosmonavtika i Raketostroenie, No. 3(28), pp. 202-214, 2002. |
| 6. | D. L. Bykov,
"On taking into account damage in filled polymer materials,"
Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 19-28, 1998. |
| 7. | D. L. Bykov,
"Modelling damage accumulation in filled polymers,"
Fatigue and Fracture of Eng. Mater. and Struct., Vol. 22, No. 11,
pp. 981-988, 1999. |
| 8. | E. Polak, Optimization: Algorithms and Consistent Approximation,
Springer-Verlag, New York, 1997. |
| 9. | A. A. Il'yushin and B. E. Pogedrya,
Fundamentals of Mathematical Thermoviscoelasticity [in Russian],
Nauka, Moscow, 1970. |
|
| Received |
03 March 2003 |
| << Previous article | Volume 38, Issue 3 / 2003 | Next article >> |
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