مدل سازی رفتار مواد هایپرالاستیک تراکم ناپذیر مدرج تابعی تحت بارگذاری خمشی

[1] Y. Anani, G.H. Rahimi, Modeling of hyperelastic behavior of functionally graded rubber under mechanical and thermal load, (2016).

[2] L. R. G. Terloar, The Physics of Rubber Elasticity, Oxford University Press, New York, (2005).

[3] E. M. Arruda, M. C. Boyce, A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, Journal of the Mechanics and Physics of Solids, 41(2) (1993) 389-412.

[4] H. M. James, E. Guth, Theory of the elastic properties of rubber, The Journal of Chemical Physics, 11(10) (1943) 455-481.

[5]  P. Flory, Theory of elasticity of polymer networks. The effect of local constraints on junctions, The Journal of Chemical Physics, 66(12) (1977) 5720-5729.

[6] F.  T.  Wall, P.  J. Flory, Statistical thermodynamics of rubber  elasticity, The  Journal  of  Chemical Physics, 19(12) (1951) 1435-1439.

[7] L. A., A Constitutive Model for Carbon Black Filled Rubber: Experimental Investigation and Mathematical Representation, j. of Continuum Mechanics and Thermodynamics, 8(3) (1996) 153-169.

[8] T. J. Van Dyke, A. Hoger, A comparison of second- order constitutive theories for hyperelastic materials, International journal of solids and structures, 37(41) (2000) 5873-5917.

[9] B. Meissner, L. Matějka, Comparison of recent rubber- elasticity theories with biaxial  stress–strain  data:  the slip-link theory of Edwards and Vilgis, Polymer, 43(13) (2002) 3803-3809.

[10] M. M. Attard, Finite strain––isotropic hyperelasticity, International Journal of Solids and Structures, 40(17) (2003) 4353-4378.

[11] M. M. Attard, G. W. Hunt, Hyperelastic constitutive modeling under finite strain, International Journal of Solids and Structures, 41(18-19) (2004) 5327-5350.

[12] L. Treloar, Stress-strain data for vulcanised rubber under various types of deformation, Transactions of the Faraday Society, 40 (1944) 59-70.

[13] M. M. Attard, Finite strain––beam theory, International journal of solids and structures, 40(17) (2003) 4563-4584.

[14] M. M. Attard, G. W. Hunt, Column buckling with shear deformations—a hyperelastic formulation, International Journal of Solids and Structures, 45(14- 15) (2008) 4322-4339.

[15] M. M. Attard, M. Y. Kim, Lateral buckling of beams with shear deformations–A hyperelastic formulation, International Journal of Solids and Structures, 47(20) (2010) 2825-2840.

[16] Y. Anani, Behavioral Modeling of Large-Deformed Rubber Based on the Model of Visco-Hyperelastic and Comparison with Experimental Results, Master’s Thesis, Mechanical Engineering of Sharif University of Technology (2007).

[17] A. Z. Kafi M. A., Bazaz M., Use of Hyperelastic materials to increase the stiffness of braces, First National Conference on Structural and Steel, Steel Structures Association of Iran, Tehran, (2010).

[18] M. Saje, G. Jelenić, Finite element formulation of hyperelastic plane frames subjected to nonconservative loads, Computers & structures, 50(2) (1994) 177-189.

[19] H. Altenbach, V. Eremeyev, On the effective stiffness of plates made of hyperelastic materials with initial stresses, International Journal of Non-Linear Mechanics, 45(10) (2010) 976-981.

[20] N. Kumar, A. DasGupta, On the contact problem   of an inflated spherical hyperelastic membrane, International Journal of Non-Linear Mechanics, 57 (2013) 130-139.

[21] A. J. Gil, Structural analysis of prestressed Saint to moderate strains, Computers & structures, 84(15-16) (2006) 1012-1028.

[22]   A. J. Gil, B. J., Wrinkling analysis of prestressed hyperelastic Saint Venant-Kirchhoff membranes, In: Metro R, editor. Shell and spatial structures: from models to realization. IASS, (2004).

[23]   E. S. Flores, S. Adhikari, M. Friswell, F. Scarpa, Hyperelastic finite element model for single wall carbon nanotubes in tension, Computational Materials Science, 50(3) (2011) 1083-1087.

[24]     E. Bilgili, Modelling mechanical behaviour of continuously graded vulcanised rubbers, Plastics, rubber and composites, 33(4) (2004) 163-169.

[25]   R. Batra, Finite plane strain deformations of rubberlike materials, International Journal for Numerical Methods in Engineering, 15(1) (1980) 145- 156.

[26]   E. Bilgili, Controlling the stress–strain inhomogeneities in axially sheared and radially heated hollow rubber tubes via functional grading, Mechanics Research Communications, 30(3) (2003) 257-266.

[27]    R. Batra, Optimal design of functionally graded incompressible linear elastic cylinders and spheres, AIAA journal, 46(8) (2008) 2050-2057.

[28]    G. Nie, R. Batra, Material tailoring and analysis    of functionally graded isotropic and incompressible linear elastic hollow cylinders, Composite structures, 92(2) (2010) 265-274.

[29]    G. Nie, R. Batra, Exact solutions and material tailoring for functionally graded hollow circular cylinders, Journal of Elasticity, 99(2) (2010) 179-201.

[30]   G. Nie, Z. Zhong, R. Batra, Material tailoring for functionally graded hollow cylinders and spheres, Composites Science and Technology, 71(5) (2011) 666-673.

[31]   R. Batra, Material tailoring and universal relations for axisymmetric deformations of functionally graded rubberlike cylinders and spheres, Mathematics and Mechanics of Solids, 16(7) (2011) 729-738.

[32]  R. Batra, Material tailoring in finite torsional Venant–Kirchhoff hyperelastic membranes subjected deformations of axially graded Mooney–Rivlin circular cylinder, Mathematics and Mechanics of Solids, 20(2) (2015) 183-189.

[33] Y. Anani, R. Naghdabadi, R. Avazmohammadi, Modeling of visco-hyperelastic behavior of foams in uniaxial tension, Proceedings of The 16th International Conference on Iranian Society of Mechanical Engineering(ISME 2008) Kerman, Iran. (in Persian), (2008).

[34] Y. Anani, R. Naghdabadi, Modeling of visco- hyperelastic behavior of rubbers in uniaxial tension, Proceedings of 7th Conference of Iranian Aerospace Society(AERO 2008), Tehran, Iran. (in persian) (2008).

[35] Y. Anani, G. H. Rahimi, Field equations and general solution for axisymmetric thick shell composed of functionally graded incompressible hyperelastic materials, International Journal of Mechanical Sciences, (2017).

[36]  L. M. Kanner, C. O. Horgan, Plane strain bending of strain-stiffening rubber-like rectangular beams, in: International Journal of Solids and Structures, 2008, pp. 1713-1729.

[37]  Y. B. Fu, R. W. Ogden, Nonlinear elasticity: theory and applications, Cambridge University Press, 2001.

[38]  L. Meunier, G. Chagnon, D. Favier, L. Orgéas, P. Vacher, Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber, Polymer Testing, 27(6) (2008) 765-777.

[39]  A. A. Khan, M. Naushad Alam, M. Wajid, Finite element modelling for static and free vibration response of functionally graded beam, Latin American Journal of Solids and Structures, 13(4) (2016) 690- 714.

[40]  M. Foroutan, R. Moradi-Dastjerdi, R. Sotoodeh- Bahreini, Static analysis of FGM cylinders by a mesh- free method, Steel & Composite Structures, 12(1) (2012) 1-11.

[9]  

[1] Y. Anani, G.H. Rahimi, Modeling of hyperelastic behavior of functionally graded rubber under mechanical and thermal load, (2016).

[2] L. R. G. Terloar, The Physics of Rubber Elasticity, Oxford University Press, New York, (2005).

[3] E. M. Arruda, M. C. Boyce, A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, Journal of the Mechanics and Physics of Solids, 41(2) (1993) 389-412.

[4] H. M. James, E. Guth, Theory of the elastic properties of rubber, The Journal of Chemical Physics, 11(10) (1943) 455-481.

[5]P. Flory, Theory of elasticity of polymer networks. The effect of local constraints on junctions, The Journal of Chemical Physics, 66(12) (1977) 5720-5729.

[6]F.  T.  Wall, P.  J. Flory, Statistical thermodynamics of rubber  elasticity, The  Journal  of  Chemical Physics, 19(12) (1951) 1435-1439.

[7] L. A., A Constitutive Model for Carbon Black Filled Rubber: Experimental Investigation and Mathematical Representation, j. of Continuum Mechanics and Thermodynamics, 8(3) (1996) 153-169.

[8] T. J. Van Dyke, A. Hoger, A comparison of second- order constitutive theories for hyperelastic materials, International journal of solids and structures, 37(41) (2000) 5873-5917.

[9] B. Meissner, L. Matějka, Comparison of recent rubber- elasticity theories with biaxial  stress–strain  data:  the slip-link theory of Edwards and Vilgis, Polymer, 43(13) (2002) 3803-3809.

[10] M. M. Attard, Finite strain––isotropic hyperelasticity, International Journal of Solids and Structures, 40(17)(2003) 4353-4378.

[11] M. M. Attard, G. W. Hunt, Hyperelastic constitutive modeling under finite strain, International Journal of Solids and Structures, 41(18-19) (2004) 5327-5350.

[12] L. Treloar, Stress-strain data for vulcanised rubber under various types of deformation, Transactions of the Faraday Society, 40 (1944) 59-70.

[13] M. M. Attard, Finite strain––beam theory, International journal of solids and structures, 40(17) (2003) 4563-4584.

[14] M. M. Attard, G. W. Hunt, Column buckling with shear deformations—a hyperelastic formulation, International Journal of Solids and Structures, 45(14- 15) (2008) 4322-4339.

[15] M. M. Attard, M. Y. Kim, Lateral buckling of beams with shear deformations–A hyperelastic formulation, International Journal of Solids and Structures, 47(20) (2010) 2825-2840.

[16] Y. Anani, Behavioral Modeling of Large-Deformed Rubber Based on the Model of Visco-Hyperelastic and Comparison with Experimental Results, Master’s Thesis, Mechanical Engineering of Sharif University of Technology (2007).

[17] A. Z. Kafi M. A., Bazaz M., Use of Hyperelastic materials to increase the stiffness of braces, First National Conference on Structural and Steel, Steel Structures Association of Iran, Tehran, (2010).

[18] M. Saje, G. Jelenić, Finite element formulation of hyperelastic plane frames subjected to nonconservative loads, Computers & structures, 50(2) (1994) 177-189.

[19] H. Altenbach, V. Eremeyev, On the effective stiffness of plates made of hyperelastic materials with initial stresses, International Journal of Non-Linear Mechanics, 45(10) (2010) 976-981.

[20] N. Kumar, A. DasGupta, On the contact problem   of an inflated spherical hyperelastic membrane, International Journal of Non-Linear Mechanics, 57 (2013) 130-139.

[21] A. J. Gil, Structural analysis of prestressed Saint to moderate strains, Computers & structures, 84(15-16) (2006) 1012-1028.

[22]   A. J. Gil, B. J., Wrinkling analysis of prestressed hyperelastic Saint Venant-Kirchhoff membranes, In: Metro R, editor. Shell and spatial structures: from models to realization. IASS, (2004).

[23]   E. S. Flores, S. Adhikari, M. Friswell, F. Scarpa, Hyperelastic finite element model for single wall carbon nanotubes in tension, Computational Materials Science, 50(3) (2011) 1083-1087.

[24]     E. Bilgili, Modelling mechanical behaviour of continuously graded vulcanised rubbers, Plastics, rubber and composites, 33(4) (2004) 163-169.

[25] R. Batra, Finite plane strain deformations of rubberlike materials, International Journal for Numerical Methods in Engineering, 15(1) (1980) 145- 156.

[26] E. Bilgili, Controlling the stress–strain inhomogeneities in axially sheared and radially heated hollow rubber tubes via functional grading, Mechanics Research Communications, 30(3) (2003) 257-266.

[27] R. Batra, Optimal design of functionally graded incompressible linear elastic cylinders and spheres, AIAA journal, 46(8) (2008) 2050-2057.

[28]    G. Nie, R. Batra, Material tailoring and analysis    of functionally graded isotropic and incompressible linear elastic hollow cylinders, Composite structures, 92(2) (2010) 265-274.

[29]    G. Nie, R. Batra, Exact solutions and material tailoring for functionally graded hollow circular cylinders, Journal of Elasticity, 99(2) (2010) 179-201.

[30]   G. Nie, Z. Zhong, R. Batra, Material tailoring for functionally graded hollow cylinders and spheres, Composites Science and Technology, 71(5) (2011) 666-673.

[31]   R. Batra, Material tailoring and universal relations for axisymmetric deformations of functionally graded rubberlike cylinders and spheres, Mathematics and Mechanics of Solids, 16(7) (2011) 729-738.

[32] R. Batra, Material tailoring in finite torsional Venant–Kirchhoff hyperelastic membranes subjected deformations of axially graded Mooney–Rivlin circular cylinder, Mathematics and Mechanics of Solids, 20(2) (2015) 183-189.

[33] Y. Anani, R. Naghdabadi, R. Avazmohammadi, Modeling of visco-hyperelastic behavior of foams in uniaxial tension, Proceedings of The 16th International Conference on Iranian Society of Mechanical Engineering(ISME 2008) Kerman, Iran. (in Persian), (2008).

[34] Y. Anani, R. Naghdabadi, Modeling of visco- hyperelastic behavior of rubbers in uniaxial tension, Proceedings of 7th Conference of Iranian Aerospace Society(AERO 2008), Tehran, Iran. (in persian) (2008).

[35] Y. Anani, G. H. Rahimi, Field equations and general solution for axisymmetric thick shell composed of functionally graded incompressible hyperelastic materials, International Journal of Mechanical Sciences, (2017).

[36]  L. M. Kanner, C. O. Horgan, Plane strain bending of strain-stiffening rubber-like rectangular beams, in: International Journal of Solids and Structures, 2008, pp. 1713-1729.

[37]  Y. B. Fu, R. W. Ogden, Nonlinear elasticity: theory and applications, Cambridge University Press, 2001.

[38]  L. Meunier, G. Chagnon, D. Favier, L. Orgéas, P. Vacher, Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber, Polymer Testing, 27(6) (2008) 765-777.

[39]  A. A. Khan, M. Naushad Alam, M. Wajid, Finite element modelling for static and free vibration response of functionally graded beam, Latin American Journal of Solids and Structures, 13(4) (2016) 690- 714.

[40]  M. Foroutan, R. Moradi-Dastjerdi, R. Sotoodeh- Bahreini, Static analysis of FGM cylinders by a mesh- free method, Steel & Composite Structures, 12(1) (2012) 1-11.