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

Abstract

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.

Keywords: elastomer, vulcanization, thermodinamical conform, finite strains

Download the article (PDF-file)

References

[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