The fractal scale-invariant structure of a temporal hierarchy in the relaxation and energy dissipation processes in a visco-elastic/capillary-porous medium
DOI:
https://doi.org/10.32347/2410-2547.2023.110.277-293Keywords:
fractality, scale-invariant structure, temporal hierarchies, processes, relaxation, aftereffect, energy dissipation, internal friction, viscoelasticity, capillary-porous mediumAbstract
The phenomena of elastic aftereffects during loading/unloading of viscoelastic and capillary-porous bodies, relaxation of their stresses is accompanied by the energy accumulation and dissipation to be taken into account in the theory of oscillations which also considers the behavior of materials when the force is applied to them. The elastic aftereffect and stress relaxation forms ostensibly opposite energy processes. In the first case, under constant load deformation, the work increases in course of time, and in the second case, under constant load deformation, the work (energy) decreases. While researching on the energy dissipation in the conditions of oscillations application, i.e. within the frame of internal friction theories, one can find that some theories are based on the dependence of friction on the oscillations’ velocity, other ones establish the dependence of friction on the amplitude. Research papers are based on the hypothesis of M.M. Davydenkov, according to which the energy when subjected to oscillations depends on the amplitude and does not depend on the velocity. According to E.S. Sorokin, the theory of internal friction is poorly consistent with the theories describing the inherited properties of materials (viscoelastic and capillary-porous ones). A tendency is observed: the better a theory reflects hereditary properties, the worse this theory is adapted to describe energy losses due to oscillations.In this paper, an attempt has been made to harmonize both these theories and numerous experiments on the destruction of materials described in the academic literature. It turns out that in order to remove contradictions, it is necessary to take into account the dependence of body deformation changing in the course of time.It is shown that the hierarchy of times determining shear and bulk relaxation in viscoelastic/capillary-porous medium has a fractal (scale-invariant) structure. It was observed that the presence of time fractality eases the modeling of viscoelastic/capillary-porous bodies resulting in the universal relaxation function of a rather simple kind. In particular, for the scale-invariant distribution of relaxation characteristics medium, the application of algebraic relaxation law for viscoelastic/capillary-porous materials is possible: this resulting in rheological models and state equations with the derivatives of fractional order.
References
Ioffe A.F. O fizike i fizikakh [About physics and physicists]. Leningrad: Nauka, 1977. – P. 244.
Filin A.P. Prikladnaia mekhanika tverdogo deformiruemogo tela [Applied mechanics of solid deformable body]. – Moskva: Nauka, 1975. – V.1. – 832 p.
Davidenkov N.N. Obzor o rasseianii energii pri vibratsiiakh [Energy dissipation during oscillations overview] // Zhurnal technicheskoy fiziki. – 1938. – V. 8. – Iss. 6. – P.11.
Pisarenko G.S., Yakovlev A.P., Matveev V.V. Vibropogloshchaiushchie svoistva konstruktsionnykh materialov: spravochnik [Vibration absorbing properties of construction materials: handbook]. – Kiev: Naukova думка, 1971. – 376 p.
Sorokin Ye. S. K teorii vnutrennego treniia pri kolebaniiakh uprugikh sistem [On the theory of internal friction during oscillations of elastic systems]. – Moskva: Gosudarstvennoe izdatelstvo literatury po stroitelstvu arkhitekture i stroitelnym materialam, 1960. – P. 132.
Kittel Ch., Nait U., Ruderman M. Mekhanika [Mechanics]. - Moskva: Nauka, 1977. – V.1. – 480 p.
Ivanov N.I. Soprotivlenie materialov [Strength of materials]. – Moskva-Leningrad: GNTTL, 1942. – P. 27, 73.
Lodg А. Elastichnye zhidkosti [Elastic liquids]. – М.: Nauka, 1984.
Uilkinson U.L. Neniutonovskie zhidkosti [Non-newtonian liquids]. - М.: Mir, 1984.
Blend D. Teoriia lineinoi viazkouprugosti [Theory of linear viscoelasticity]. М.: Mir, 1965.
Slonimskii G.L. // DAN SSSR. – 1961. – V. 140. - № 2. – P. 343.
Tobolskii A. Svoistva i struktura polimerov [Properties and structure of polymers]. – М.: Himiia, 1964.
Oshbalov P.M., Mirzadzhanzade A.Kh. Mekhanika fizicheskikh protsessov [Mechanics of physical processes]. – М.: MGU, 1976.
Mirzadzhanzade A.Kh., Kovalev A.G., Zaitsev U.V. Osobennosti ekspluatatsii mestorozhdenii anomalnykh neftei [Operational features of anomalous oil fields]. - М.: Nedra, 1972.
Shulman Z.P., Khusid B.M. Nestatsionarnye protsessy konvektivnogo perenosa v nasledstvennykh sredakh [Non-stationary processes of convective transfer in hereditary media]. – Minsk: Nauka i tekhnika, 1983.
Gidrodinamika truboprovodnogo transporta nefti i nefteproduktov [Hydrodynamics of pipeline transportation of oil and oil products]. // A.Kh. Mirzadzhanzade, A.K. Galiamov, V.I. Maron i dr. – М.: Nedra, 1984.
Shlezinger M., Klafter Dzh. // V kn.: Fraktaly v fizike [Fractals in physics]. - М.: Mir, 1988. – P. 552.
Bliumen A., Klafter Dzh., Tsumofen G.// V kn.: Fraktaly v fizike [Fractals in physics]. - М.: Mir, 1988. – P. 561.
Petrov B.N., Krutko P.L. Izvestiia AN SSSR. Tekhnicheskaia kibernetika [Technique cybernetics]. – 1970. - №2. – P. 128.
Rozenvasser E.N., Iusupov R.M. Chuvstvitelnost sistem upravleniia [Sensitivity of guidance systems]. - М.: Nauka, 1981.
Rabotnov U.N. Elementy nasledstvennoi mekhaniki tverdykh tel [Elements of hereditary mechanics of solids]. - М.: Nauka, 1977.
Nigmatullin R.R.// Fizika tverdogo tela [Solid state physics]. - 1985. – V.27. – №5. – P. 1983.
Mirzadzhanzade A.Kh., Ametov I.М. Prognozirovanie promyslovoi effektivnosti metodov teplovogo vozdeistviia na neftianye plasty [Forecasting of field efficiency regarding methods of thermal effect on oil reservoirs]. - М.: Nedra, 1983.
Barenblatt G.I. i dr.// Izvestiia AN SSSR. OTN. – 1957. - №11. – P. 84.
Khimmelblau D. Analiz protsessov statisticheskimi metodami [Analysis of processes using statistical methods]. - М.: Mir, 1973.
Charnyi I.A. Neustanovivsheesia dvizhenie realnoi zhidkosti v trubakh [Unsteady motion of real liquid in pipes]. - М.: Nedra, 1975.
Barenblatt G.I., Enotov V.М., Ryzhik V.М. Teoriia nestatsionarnoi filtratsii zhidkosti i gaza [Theory of non-stationary filtration of liquid and gas]. - М.: Nedra, 1972.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
