Far Eastern Mathematical Journal

To content of the issue

A thermodynamical conform for the curing coupling in elastomer at large strains

Chekhonin K. A.

2022, issue 1, P. 107-118
DOI: https://doi.org/10.47910/FEMJ202211

In the framework of a two-component medium, the phenomenological approach is used to develop a system of constitutive equations describing the thermomechanical behavior of elastomers during curing. This model is designed to describe the stress-strain states in the temperature range comprising the intervals of phase and relaxation transitions at lage strains within a rigorous thermodinamical framework. The results of numerical experiments demonstrating the possibility of describing the characteristic properties of deformation processes typical of elastomers are given.

elastomer, vulcanization, thermodinamical conform, finite strains

Download the article (PDF-file)


[1] N. Kh. Arutiunian, A. V. Manzhirov, V. E. Naumov, Kontaktnye zadachi mekhaniki rastushchikh tel, Nauka, M., 1991, 176 s.
[2] N. Kh. Arutiunian, A. D. Drozdov, V. E. Naumov, Mekhanika rastushchikh viazkouprugoplasticheskikh tel, Nauka, M., 1987, 471 s.
[3] A. A. Il'iushin, B. E. Pobedria, Osnovy matematicheskoi teorii termoviazkouprugosti, Nauka, M., 1970, 280 s.
[4] V. V. Moskvitin, Soprotivlenie viazkouprugikh materialov, Nauka, M., 1972, 328 s. pressure, isochoric deformation and temperature.
[5] L. A. Golotina, V. P. Matveenko, I. N. Shardakov, “Analysis of deformation process charac-teristics in amorphous-crystalline polymers”, Mechanics of Solids, 47 (2012), 634–340.
[6] K. Kannan, K. Rajagopal, “A thermodynamical framework for chemically reacting systems. Zeitschrift fr Angewandte”, Mathematik und Physik (ZAMP), 62 (2011), 331–363. volumetric swelling due to a chemical reaction.
[7] S. A. Chester, L. Anand, “A thermo-mechanically coupled theory for ?uid permeation in elastomeric materials: Application to thermally responsive gels”, Journal of the Mechanics and Physics of Solids, 59:10 (2011), 1978–2006.
[8] A. V. Amirkhizi, J. Isaacs, J. McGee, S. Nemat-Nasser, “An experimentally-based viscoelastic constitutive model for polyurea, including pressure and temperature e?ects”, Philosophical Magazine, 86 (2006), 5847–5866.
[9] A. Amin, A. Lion, S. Sekita, Y. Okui, “Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: Experimental identi?cation and numerical veri?cation”, International Journal of Plasticity, 22:9 (2006), 1610–1657.
[10] J. Plagge, M. Kluppel, “A physically based model of stress softening and hysteresis of ?lled rubber including rate- and temperature dependency”, International Journal of Plasticity, 89 (2017), 173–196.
[11] E. M. Arruda, M. C. Boyce, “A 3-dimensional constitutive model for the large stretch behavior of rubber elastic materials”, Journal of the Mechanics and Physics of Solids, 41 (1993), 389–412.
[12] M. Andre, P. Wriggers, “Thermo-mechanical behaviour of rubber materials during vulcanization”, International Journal of Solids and Structures, 42:1617 (2005), 4758–4778.
[13] K. A. Chekhonin, V. D. Vlasenko, “Numerical Modelling of Compression Cure High-Filled Polimer Material”, Journal of Siberian Federal University. Mathematics & Physics, 14:6 (2021), 805–814.
[14] K. A. Chekhonin, V. D. Vlasenko, “Gradientnyi algoritm optimizatsii temperaturno-konversionnoi zadachi pri otverzhdenii vysokonapolnennykh polimernykh materialov”, Informatika i sistemy upravleniia, 4:62 (2019), 58–70.
[15] K. A. Chekhonin, V. D. Vlasenko, “The role of curing stresses in subsequent response and damage of elastomer composites”, Journal of Physics: Conference Series International Conference on Computational Mechanics and Modern Applied Software Systems (CMMASS’2021), 2021, 68–75.
[16] K. A. Chekhonin, V. D. Vlasenko, “The Role of Curing Stresses in Subsequent Response and Damage of High Energetic materials”, Journal of Physics: Conference Series. The conference on High Energy Processes in Condensed Matter (HEPCM)-2021, 2021, 55–63.
[17] V. K. Bulgakov, K. A. Chekhonin, “Modeling of a 3D Problem of compression forming system “Composite shell – low compressible consolidating Filler””, J. Mathematical Modeling, 4 (2002), 121–131.
[18] K. A. Chekhonin, “ Osnovy teorii otverzhdeniia tverdykh raketnykh topliv” , Vestnik ITPS, 12:1 (2016), 131–145.
[19] L. R. Herrmann, “Elasticity Equations for Incompressible and Nearly Incompressible Materials by a Variational Theorem”, AIAA J., 3 (1965), 1896–1900.
[20] E. Reissner, “On a variational principle for elastic displacements and pressure Incompressible Materials by a Variational Theorem”, J. Appl. Mech., 51 (1984), 444–445.
[21] V. K. Bulgakov, K. A. Chekhonin, Osnovy teorii metoda smeshannykh konechnykh elementov, Izd-vo Khabar. tekhn. un-t, Khabarovsk, 1999, 357 s.

To content of the issue