The Nonlinear Thermo-Hyperelastic Analysis of Functionally Graded Incompressible Hollow Sphere with Temperature Dependent Material Using Finite Element Method
محورهای موضوعی : Mechanics of Solids
Ali Zargaripoor
1
,
Mohammad Shariyat
2
1 - دانشگاه خواجه نصیرالدین طوسی
2 - KNT University of tehran
کلید واژه: Hyperelastic, Functionally graded material, Temperature dependent material, ,
چکیده مقاله :
In this paper, a nonlinear finite element formulation is presented for analysis of the stress, displacement, and temperature distributions of thermo hyperelastic hollow spheres subjected to mechanical and thermal forces. It is assumed that the hollow sphere is made of functionally graded and temperature-dependent material. The coupled nonlinear equations are derived from the concept of multiplicative decomposition of the deformation gradient. Mechanical and thermal parts are considered for studying the thermo-hyperelastic behavior.An appropriate strain energy function is considered and by exchange the invariants of strain tensors in the modified model, the governing equations are extended to an incompressible model. The governing equations are found by considering Mooney-Rivlin hyperelastic model. Distribution of displacement, stress components, and temperature through the thickness of the hollow sphere are plotted for different constitutive, temperature dependency, and inhomogeneity parameters. The obtained results indicate that the temperature dependency of the material and inhomogeneity properties have a considerable influence on displacement, stress components, and temperature distribution along the radial direction.
In this paper, a nonlinear finite element formulation is presented for analysis of the stress, displacement, and temperature distributions of thermo hyperelastic hollow spheres subjected to mechanical and thermal forces. It is assumed that the hollow sphere is made of functionally graded and temperature-dependent material. The coupled nonlinear equations are derived from the concept of multiplicative decomposition of the deformation gradient. Mechanical and thermal parts are considered for studying the thermo-hyperelastic behavior.An appropriate strain energy function is considered and by exchange the invariants of strain tensors in the modified model, the governing equations are extended to an incompressible model. The governing equations are found by considering Mooney-Rivlin hyperelastic model. Distribution of displacement, stress components, and temperature through the thickness of the hollow sphere are plotted for different constitutive, temperature dependency, and inhomogeneity parameters. The obtained results indicate that the temperature dependency of the material and inhomogeneity properties have a considerable influence on displacement, stress components, and temperature distribution along the radial direction.
[1] B. Kim, S. B. Lee, J. Lee, S. Cho, H. Park, S. Yeom, S. H. Park, A comparison among Neo-Hookean model, Mooney-Rivlin model, and Ogden model for chloroprene rubber, International Journal of Precision Engineering and Manufacturing, Vol. 13, pp. 759-764, 2012.
[2] M. Mooney, A theory of large elastic deformation, Journal of applied physics, Vol. 11, No. 9, pp. 582-592, 1940.
[3] R. W. Ogden, Large deformation isotropic elasticity–on the correlation of theory and experiment for incompressible rubberlike solids, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Vol. 326, No. 1567, pp. 565-584, 1972.
[4] D. Taghizadeh, A. Bagheri, H. Darijani, On the hyperelastic pressurized thick-walled spherical shells and cylindrical tubes using the analytical closed-form solutions, International Journal of Applied Mechanics, Vol. 7, No. 02, pp. 1550027, 2015.
[5] D. Aranda-Iglesias, G. Vadillo, J. A. Rodríguez-Martínez, Constitutive sensitivity of the oscillatory behaviour of hyperelastic cylindrical shells, Journal of Sound and Vibration, Vol. 358, pp. 199-216, 2015.
[6] I. D. Breslavsky, M. Amabili, M. Legrand, Static and dynamic behavior of circular cylindrical shell made of hyperelastic arterial material, Journal of Applied Mechanics, Vol. 83, No. 5, pp. 051002, 2016.
[7] Y. Anani, G. H. Rahimi, Stress analysis of rotating cylindrical shell composed of functionally graded incompressible hyperelastic materials, International Journal of Mechanical Sciences, Vol. 108, pp. 122-128, 2016.
[8] K. Narooei, M. Arman, Modification of exponential based hyperelastic strain energy to consider free stress initial configuration and Constitutive modeling, Journal of Computational Applied Mechanics, Vol. 49, No. 1, pp. 189-196, 2018.
[9] A. Ataee, R. Noroozi, Behavioral optimization of pseudo-neutral hole in hyperelastic membranes using functionally graded cables, Journal of Computational Applied Mechanics, Vol. 49, No. 2, pp. 282-291, 2018.
[10] H. Gharooni, M. Ghannad, Nonlinear analytical solution of nearly incompressible hyperelastic cylinder with variable thickness under non-uniform pressure by perturbation technique, Journal of Computational Applied Mechanics, Vol. 50, No. 2, pp. 395-412, 2019.
[11] H. Gharooni, M. Ghannad, Nonlinear analysis of radially functionally graded hyperelastic cylindrical shells with axially-varying thickness and non-uniform pressure loads based on perturbation theory, Journal of Computational Applied Mechanics, Vol. 50, No. 2, pp. 324-340, 2019.
[12] Y. Anani, G. Rahimi, On the stability of internally pressurized thick-walled spherical and cylindrical shells made of functionally graded incompressible hyperelastic material, Latin American Journal of Solids and Structures, Vol. 15, pp. e37, 2018.
[13] M. Shariyat, M. Khosravi, M. Y. Ariatapeh, M. Najafipour, Nonlinear stress and deformation analysis of pressurized thick-walled hyperelastic cylinders with experimental verifications and material identifications, International Journal of Pressure Vessels and Piping, Vol. 188, pp. 104211, 2020.
[14] Z. Zhao, D. Niu, H. Zhang, X. Yuan, Nonlinear dynamics of loaded visco-hyperelastic spherical shells, Nonlinear Dynamics, Vol. 101, pp. 911-933, 2020.
[15] S. Jemioło, A. Franus, Finite Element Method Modelling of Long and Short Hyperelastic Cylindrical Tubes, in Proceeding of, Springer, pp. 152-160.
[16] F. Aghaienezhad, R. Ansari, M. Darvizeh, On the stability of hyperelastic spherical and cylindrical shells subjected to external pressure using a numerical approach, International Journal of Applied Mechanics, Vol. 14, No. 10, pp. 2250094, 2022.
[17] A. Anssari-Benam, A. Bucchi, G. Saccomandi, Modelling the inflation and elastic instabilities of rubber-like spherical and cylindrical shells using a new generalised neo-Hookean strain energy function, Journal of Elasticity, Vol. 151, No. 1, pp. 15-45, 2022.
[18] H. B. Khaniki, M. H. Ghayesh, Highly nonlinear hyperelastic shells: Statics and dynamics, International Journal of Engineering Science, Vol. 183, pp. 103794, 2023.
[19] Z. Yosibash, D. Weiss, S. Hartmann, High-order FEMs for thermo-hyperelasticity at finite strains, Computers & Mathematics with Applications, Vol. 67, No. 3, pp. 477-496, 2014.
[20] A. Almasi, M. Baghani, A. Moallemi, Thermomechanical analysis of hyperelastic thick-walled cylindrical pressure vessels, analytical solutions and FEM, International Journal of Mechanical Sciences, Vol. 130, pp. 426-436, 2017.
[21] J. Xu, X. Yuan, H. Zhang, Z. Zhao, W. Zhao, Combined effects of axial load and temperature on finite deformation of incompressible thermo-hyperelastic cylinder, Applied Mathematics and Mechanics, Vol. 40, No. 4, pp. 499-514, 2019.
[22] M. Mirparizi, A. Fotuhi, Nonlinear coupled thermo-hyperelasticity analysis of thermal and mechanical wave propagation in a finite domain, Physica A: Statistical Mechanics and its Applications, Vol. 537, pp. 122755, 2020.
[23] F. Shakeriaski, M. Ghodrat, J. Escobedo-Diaz, M. Behnia, The nonlinear thermo-hyperelasticity wave propagation analysis of near-incompressible functionally graded medium under mechanical and thermal loadings, Archive of Applied Mechanics, Vol. 91, No. 7, pp. 3075-3094, 2021.
[24] R. Wang, H. Ding, X. Yuan, N. Lv, L. Chen, Nonlinear singular traveling waves in a slightly compressible thermo-hyperelastic cylindrical shell, Nonlinear Dynamics, pp. 1-15, 2022.
[25] A. Bakhtiyari, M. Baniasadi, M. Baghani, A modified constitutive model for shape memory polymers based on nonlinear thermo-visco-hyperelasticity with application to multi-physics problems, International Journal of Applied Mechanics, Vol. 15, No. 04, pp. 2350032, 2023.
[26] S. Lu, K. Pister, Decomposition of deformation and representation of the free energy function for isotropic thermoelastic solids, International Journal of Solids and Structures, Vol. 11, No. 7-8, pp. 927-934, 1975.
[27] W. Ehlers, G. Eipper, The simple tension problem at large volumetric strains computed from finite hyperelastic material laws, Acta Mechanica, Vol. 130, No. 1-2, pp. 17-27, 1998.
[28] M. Shojaeifard, K. Wang, M. Baghani, Large deformation of hyperelastic thick-walled vessels under combined extension-torsion-pressure: analytical solution and FEM, Mechanics Based Design of Structures and Machines, Vol. 50, No. 12, pp. 4139-4156, 2022.
[29] A. F. Bower, 2009, Applied mechanics of solids, CRC press,
