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Kinematics and kinetics modeling of thermoelastic continua based on the multiplicative decomposition of the deformation gradient. (English) Zbl 1423.74011

Summary: Solids usually show complex material behavior. If deformation is finite, the description of the kinematics makes the mechanical model complicated. In fact, one of the basic questions in the formulation and analysis procedures of finite deformation thermoelasticity is: “How can the finite deformation thermoelasticity response be best accounted for in the kinematic formulation?” A rather attractive way to proceed is to use the approach of small strain analysis, and decompose the total strain into a mechanical part and a thermal part. In this paper, based on the multiplicative decomposition of the deformation gradient, the mechanical and thermal strains are defined in the power and exponential forms. Also, the decomposition of the total strain into the mechanical and thermal strains is investigated for extension of various constitutive models at small deformation to the finite deformation thermoelasticity. In order to model the mechanical behavior of thermoelastic continua in the stress-producing process of nonisothermal deformation, an isothermal effective stress-strain equation based on the proposed strains is considered. Regards to this constitutive equation and assuming a linear dependence of the specific heat on temperature, the state functions including the internal energy, free energy, entropy and stress tensor are derived in the case of finite deformation thermoelasticity. Based on this decomposition and the proposed strains, it can be seen that these state functions are an extension from small deformation to finite deformation thermoelasticity. In addition, the mechanical and thermal material parameters are determined using the mechanical tests done at constant and the free thermal expansion test data, respectively.

MSC:

74A05 Kinematics of deformation
74B05 Classical linear elasticity
74F05 Thermal effects in solid mechanics
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[1] I-Shih, Liu, Continuum mechanics, (2002), Springer Berlin, Heidelberg, New York · Zbl 1058.74004
[2] Hill, R., On constitutive inequalities for simple materials, Journal of the Mechanics and Physics of Solids, 16, 229-242, (1968) · Zbl 0162.28702
[3] Hill, R., Aspects of invariance in solid mechanics, Advances in Applied Mechanics, 18, 1-75, (1978) · Zbl 0475.73026
[4] Seth, B. R., Generalized strain measures with application to physical problems, (Second-order effects in elasticity, Plasticity and fluid dynamics, Vol. 415, (1964), Pergamon Oxford), 162-172
[5] Darijani, H.; Naghdabadi, R., Constitutive modeling of solids at finite deformation using a second-order stress–strain relation, International Journal of Engineering Science, 48, 223-236, (2010)
[6] Eckart, C., The thermodynamics of irreversible processes, IV: the theory of elasticity and anelasticity, Physical Review, 73, 373-380, (1948) · Zbl 0032.22201
[7] Kroner, E., Allgemeine kontinuumstheorie der versetzungen und eigensspannungen, Archive for Rational Mechanics and Analysis, 4, 273-334, (1960) · Zbl 0090.17601
[8] Sedov, L., Foundations of the non-linear mechanics of continua, (1966), Pergamon Press Oxford · Zbl 0137.19502
[9] Stojanovic, R.; Djuric, S.; Vujosevic, L., On finite thermal deformations, Archives of Mechanics: Stosowanej, 16, 103-108, (1964) · Zbl 0134.44301
[10] Holzapfel, G. A., Nonlinear solid mechanics, A continuum approach for engineering, (2000), John Wiley & Sons Chichester · Zbl 0980.74001
[11] Wunderlich, B., Thermal analysis of polymeric materials, (2005), Springer New York
[12] Gaur, U.; Shu, H. C.; Wunderlich, B., Heat capacity and other thermodynamic properties of linear macromolecules, Journal of Physical and Chemical Reference Data, 12, 91-108, (1983)
[13] Lubarda, V. A., On thermodynamic potentials in linear thermoelasticity, International Journal of Solids and Structures, 41, 7377-7398, (2004) · Zbl 1076.74003
[14] Darijani, H.; Naghdabadi, R., Hyperelastic materials behavior modeling using consistent strain energy density functions, Acta Mechanica, 213, 235-254, (2010) · Zbl 1397.74022
[15] Valanis, K. C.; Landel, R. F., The strain-energy function of hyper-elastic material in terms of extension ratios, Journal of Applied Physics, 38, 2997-3002, (1967)
[16] Bradley, G. L.; Chang, P. C.; Mckenna, G. B., Rubber modeling using uniaxial test data, Journal of Applied Polymer Science, 81, 837-848, (2001)
[17] Bischoff, J. E.; Arruda, E. M.; Grosh, K., A new constitutive model for the compressibility of elastomers at finite deformations, Rubber Chemistry and Technology, 74, 541-559, (2000)
[18] Ogden, R. W., Non-linear elastic deformations, (1997), Dover Publications, Inc. Mineola, New York
[19] Kawabata, S.; Matsuda, M.; Tel, K.; Kawai, H., Experimental survey of the strain energy density function of isoprene rubber vulcanizate, Macromolecules, 14, 154-162, (1981)
[20] Heuillet, P.; Dugautier, L., Modelisation du comportement hyperelastique des caoutchoucs et elastomeres thermoplastiques compacts on cellulaires, Genie Mecanique des Caoutchoucs et des Elastomeres Thermoplastiques, (1997)
[21] El-Ratal, W. H.; Mallick, P. K., Elastic response of flexible polyurethane foams in uniaxial tension, Journal of Engineering Materials and Technology-Transactions of the ASME, 118, 157-161, (1996)
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