Abstract
This paper is dedicated to the solution of a coupled problem on creep and viscoplastic flow in a flat heavy layer. The layer is on an inclined surface and subject to heating and cooling. The problem has been solved in the framework of the large elastoplastic strain mathematical model, which generalized for the case of taking into account rheological and thermophysical material properties. The thermophysical and deformation processes are interconnected; a yield limit, a viscosity factor and creep parameters depend on temperature. The patterns of the motion of elastoplastic boundaries are shown, stresses, strains and strain rates in the areas of flow and thermoviscoelastic deformation has been calculated.
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REFERENCES
E. H. Lee, ‘‘Elastic-plastic deformation at finite strains,’’ J. Appl. Mech. 36, 1–6 (1969).
V. I. Kondaurov, ‘‘Equations of elastoviscoplastic medium with finite deformations,’’ J. Appl. Mech. Tech. Phys. 23, 584–591 (1982).
A. A. Pozdeev, P. V. Trusov, and Yu. I. Nyashin, Large Elastoplastic Deformations: Theory, Algorithms, Applications (Nauka, Moscow, 1986) [in Russian].
A. A. Rogovoi, ‘‘Constitutive relations for finite elastic-inelastic strains,’’ J. Appl. Mech. Tech. Phys. 46, 730–739 (2005).
V. I. Levitas, Large Elastoplastic Deformations of Materials at High Pressure (Naukova Dumka, Kiev, 1987) [in Russian].
Yu. I. Dimitrienko, Nonlinear Continuum Mechanics (Fizmatlit, Moscow, 2009) [in Russian].
A. I. Golovanov and L. U. Sultanov, Mathematical Models of Computational Nonlinear Solid Mechanics (Kazan. Gos. Univ., Kazan, 2009) [in Russian].
P. M. Naghdi, ‘‘A critical review of the state of finite plasticity,’’ J. Appl. Phys. 41, 315–394 (1990).
J. C. Simo, ‘‘A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Part I. Continuum formulation,’’ Comput. Methods Appl. Mech. Eng. 66, 199–219 (1988).
H. Xiao, O. T. Bruhns, and A. Meyers, ‘‘A consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and deformation gradient,’’ Int. J. Plast. 16, 143–177 (2000).
M. R. Pietryga, S. Reese, and I. N. Vladimirov, ‘‘Anisotropic finite elastoplasticity with nonlinear kinematic and isotropic hardeningand application to sheet metal forming,’’ Int. J. Plast. 26, 659–687 (2010).
A. V. Shutov and J. Ihlemann, ‘‘Analysis of some basic approaches to finite strain elasto-plasticity in view of reference change,’’ Int. J. Plast. 63, 183–197 (2014).
A. V. Shutov, A. Yu. Larichkin, and V. A. Shutov, ‘‘Modelling of cyclic creep in the finite strain range using a nested split of the deformation gradient,’’ Zeitschr. Angew. Math. Mech. 97, 1083–1099 (2017).
V. P. Myasnikov, ‘‘Equations of motion of elastoplastic materials at large deformations,’’ Vestn. DVO RAN 4, 8–13 (1996).
G. I. Bykovtsev and A. V. Shitikov, ‘‘Finite deformations in an elastoplastic medium,’’ Dokl. Akad. Nauk SSSR 311, 59–62 (1990).
A. A. Burenin, G. I. Bykovtsev, and L. V. Kovtanyuk, ‘‘A simple model of finite strain in an elastoplastic medium,’’ Dokl. Phys. 41, 127–129 (1996).
A. A. Burenin, L. V. Kovtanyuk, and G. L. Panchenko, ‘‘Modeling of large elastoviscoplastic deformations with thermophysical effects taken into account,’’ Mech. Solids 45, 583–594 (2010).
L. V. Kovtanyuk and A. V. Shitikov, ‘‘On the theory of large elastoplastic deformations of materials with temperature and rheological effects taken into account,’’ Vestn. DVO RAN 4, 87–93 (2006).
A. A. Burenin and L. V. Kovtanyuk, Large Irreversible Strains and Elastic Aftereffect (Dalnauka, Vladivostok, 2013) [in Russian].
L. V. Kovtanyuk and G. L. Panchenko, ‘‘Nonisothermal deformation of an elastoviscoplastic flat heavy layer,’’ J. Appl. Ind. Math. 7, 396–403 (2013).
S. V. Belykh, K. S. Bormotin, A. A. Burenin, L. V. Kovtanyuk, and A. N. Prokudin, ‘‘On large isothermal deformation of materials with elastic, viscous and plastic properties,’’ Vestn. Chuvash Ped. Univ., Ser. Mekh. Predel. Sost. 4 (22), 144–156 (2014).
A. S. Begun, A. A. Burenin, and L. V. Kovtanyuk, ‘‘Large irreversible deformations under conditions of changing mechanisms of their formation and the problem of definition of plastic potentials,’’ Dokl. Phys. 61, 463–466 (2016).
I. Alain, ‘‘The correlation between the power-law coefficients in creep: the temperature dependence,’’ J. Mater. Sci. 33, 3201–3206 (1998).
F. Pla, A. M. Mancho, and H. Herrero, ‘‘Bifurcation phenomena in a convection problem with temperature dependent viscosity at low aspect ratio,’’ Phys. D: Nonlin. Phenom. 238, 572–580 (2009).
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Kovtanyuk, L.V., Panchenko, G.L. Mathematical Modelling of the Production Process of Irreversible Strains Under the Heating and Cooling of a Flat Heavy Layer on an Inclined Surface. Lobachevskii J Math 42, 1998–2005 (2021). https://doi.org/10.1134/S1995080221080163
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DOI: https://doi.org/10.1134/S1995080221080163