How to cite this paper
Franus, A & Jemioło, S. (2022). Consistent polynomial expansions of the stored energy function for incompressible hyperelastic materials.Engineering Solid Mechanics, 10(4), 351-360.
Refrences
Anssari-Benam, A., & Bucchi, A. (2021). A generalised neo-Hookean strain energy function for application to the finite deformation of elastomers. International Journal of Non-Linear Mechanics, 128, 103626.
Attard, M. M., & Hunt, G. W. (2004). Hyperelastic constitutive modeling under finite strain. International Journal of Solids and Structures, 41(18-19), 5327-5350.
Ball, J. M. (1976). Convexity conditions and existence theorems in nonlinear elasticity. Archive for rational mechanics and Analysis, 63(4), 337-403.
Bauman, J. T. (2008). Strain of Rubber Components: Guide for Design Engineers. Hanser, Munich, Germany.
Biderman, V. L. (1958). Calculation of rubber parts. Rascheti na prochnost, 40.
Bonet, J., Gil, A. J., & Wood, R. D. (2016). Nonlinear solid mechanics for finite element analysis: statics. Cambridge University Press.
Ciarlet, P. G. (1988). Three-dimensional elasticity. Elsevier.
Currie, P. K. (2004). The attainable region of strain-invariant space for elastic materials. International Journal of Non-Linear Mechanics, 39(5), 833-842.
Currie, P. K. (2005). Comparison of incompressible elastic strain energy functions over the attainable region of invariant space. Mathematics and mechanics of solids, 10(5), 559-574.
Darijani, H., & Naghdabadi, R. (2010). Hyperelastic materials behavior modeling using consistent strain energy density functions. Acta mechanica, 213(3), 235-254.
Dassault Systèmes, (2015). Abaqus 2016 Theory Guide.
Destrade, M., Saccomandi, G., & Sgura, I. (2017). Methodical fitting for mathematical models of rubber-like materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2198), 20160811.
Franus, A., Jemioło, S., & Antoni, M. (2020). A slightly compressible hyperelastic material model implementation in ABAQUS. Engineering Solid Mechanics, 8(4), 365-380.
Horgan, C. O. (2021). A note on a class of generalized neo-Hookean models for isotropic incompressible hyperelastic materials. International Journal of Non-Linear Mechanics, 129, 103665.
Horgan, C. O., & Murphy, J. G. (2009). On the volumetric part of strain-energy functions used in the constitutive modeling of slightly compressible solid rubbers. International Journal of Solids and Structures, 46(16), 3078-3085.
Isihara, A., Hashitsume, N., & Tatibana, M. (1951). Statistical theory of rubber‐like elasticity. IV.(two‐dimensional stretching). The Journal of Chemical Physics, 19(12), 1508-1512.
James, A. G., Green, A., & Simpson, G. M. (1975). Strain energy functions of rubber. I. Characterization of gum vulcanizates. Journal of Applied Polymer Science, 19(7), 2033-2058.
Jemiolo, S. (2019, November). Instability of a square sheet of rubberlike material under symmetric biaxial stretching. In IOP Conference Series: Materials Science and Engineering (Vol. 661, No. 1, p. 012031). IOP Publishing.
Jemioło, S. (2002). Studium hipersprężystych własności materiałów izotropowych: Modelowanie i implementacja numeryczna. Oficyna Wydawnicza PW.
Liu, I.-S. (2002). Continuum Mechanics, Springer-Verlag Berlin.
Marckmann, G., & Verron, E. (2006). Comparison of hyperelastic models for rubber-like materials. Rubber chemistry and technology, 79(5), 835-858.
Mooney, M. (1940). A theory of large elastic deformation. Journal of applied physics, 11(9), 582-592.
Ogden, R. W. (1976). Volume changes associated with the deformation of rubber-like solids. Journal of the Mechanics and Physics of Solids, 24(6), 323-338.
Rivlin, R. S. (1948). Large elastic deformations of isotropic materials. 1. Fundamental concepts. Philosophical Transactions of the Royal Society of London Series a-Mathematical and Physical Sciences, 240(822), 459-508.
Sato, Y. (1970). On the Second Order Approximation in the Phenomenological Theory of Large Elastic Deformation. Journal of Society of Material Science of Japan, 19, 322-325.
Sato, Y. (1978). Construction of a Hierarchy of Approximation of Elasticity Theory of Finite Deformation. Nihon Reoroji Gakkaishi (Journal Soc. Rheol. Japan), 6, 58-78.
Seibert, D. J., & Schoche, N. (2000). Direct comparison of some recent rubber elasticity models. Rubber chemistry and technology, 73(2), 366-384.
Sharma, S. (2003). Critical comparison of popular hyper-elastic material models in design of anti-vibration mounts for automotive industry through FEA. Constitutive Models for Rubber, 161-168.
Suchocki, C., & Jemioło, S. (2020). On finite element implementation of polyconvex incompressible hyperelasticity: theory, coding and applications. International Journal of Computational Methods, 17(08), 1950049.
Tabaddor, F. (1987). Rubber elasticity models for finite element analysis. Computers & Structures, 26(1-2), 33-40.
Treloar, L. R. G. (1944). Stress-strain data for vulcanized rubber under various types of deformation. Rubber Chemistry and Technology, 17(4), 813-825.
Tschoegl, N. W. ( 1971). Constitutive equations for elastomers. Journal of Polymer Science Part A-1: Polymer Chemistry, 9(7), 1959-1970.
Van der Hoff, B. M. E., & Buckler, E. J. (1967). Transient changes in topology and energy on extension of polybutadiene networks. Journal of Macromolecular Science—Chemistry, 1(4), 747-788.
Yeoh, O. H. (1990). Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber chemistry and technology, 63(5), 792-805.
Zahorski, S. (1959). A form of elastic potential for rubber-like materials. Archives of Mechanics, 5, 613-617.
Attard, M. M., & Hunt, G. W. (2004). Hyperelastic constitutive modeling under finite strain. International Journal of Solids and Structures, 41(18-19), 5327-5350.
Ball, J. M. (1976). Convexity conditions and existence theorems in nonlinear elasticity. Archive for rational mechanics and Analysis, 63(4), 337-403.
Bauman, J. T. (2008). Strain of Rubber Components: Guide for Design Engineers. Hanser, Munich, Germany.
Biderman, V. L. (1958). Calculation of rubber parts. Rascheti na prochnost, 40.
Bonet, J., Gil, A. J., & Wood, R. D. (2016). Nonlinear solid mechanics for finite element analysis: statics. Cambridge University Press.
Ciarlet, P. G. (1988). Three-dimensional elasticity. Elsevier.
Currie, P. K. (2004). The attainable region of strain-invariant space for elastic materials. International Journal of Non-Linear Mechanics, 39(5), 833-842.
Currie, P. K. (2005). Comparison of incompressible elastic strain energy functions over the attainable region of invariant space. Mathematics and mechanics of solids, 10(5), 559-574.
Darijani, H., & Naghdabadi, R. (2010). Hyperelastic materials behavior modeling using consistent strain energy density functions. Acta mechanica, 213(3), 235-254.
Dassault Systèmes, (2015). Abaqus 2016 Theory Guide.
Destrade, M., Saccomandi, G., & Sgura, I. (2017). Methodical fitting for mathematical models of rubber-like materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2198), 20160811.
Franus, A., Jemioło, S., & Antoni, M. (2020). A slightly compressible hyperelastic material model implementation in ABAQUS. Engineering Solid Mechanics, 8(4), 365-380.
Horgan, C. O. (2021). A note on a class of generalized neo-Hookean models for isotropic incompressible hyperelastic materials. International Journal of Non-Linear Mechanics, 129, 103665.
Horgan, C. O., & Murphy, J. G. (2009). On the volumetric part of strain-energy functions used in the constitutive modeling of slightly compressible solid rubbers. International Journal of Solids and Structures, 46(16), 3078-3085.
Isihara, A., Hashitsume, N., & Tatibana, M. (1951). Statistical theory of rubber‐like elasticity. IV.(two‐dimensional stretching). The Journal of Chemical Physics, 19(12), 1508-1512.
James, A. G., Green, A., & Simpson, G. M. (1975). Strain energy functions of rubber. I. Characterization of gum vulcanizates. Journal of Applied Polymer Science, 19(7), 2033-2058.
Jemiolo, S. (2019, November). Instability of a square sheet of rubberlike material under symmetric biaxial stretching. In IOP Conference Series: Materials Science and Engineering (Vol. 661, No. 1, p. 012031). IOP Publishing.
Jemioło, S. (2002). Studium hipersprężystych własności materiałów izotropowych: Modelowanie i implementacja numeryczna. Oficyna Wydawnicza PW.
Liu, I.-S. (2002). Continuum Mechanics, Springer-Verlag Berlin.
Marckmann, G., & Verron, E. (2006). Comparison of hyperelastic models for rubber-like materials. Rubber chemistry and technology, 79(5), 835-858.
Mooney, M. (1940). A theory of large elastic deformation. Journal of applied physics, 11(9), 582-592.
Ogden, R. W. (1976). Volume changes associated with the deformation of rubber-like solids. Journal of the Mechanics and Physics of Solids, 24(6), 323-338.
Rivlin, R. S. (1948). Large elastic deformations of isotropic materials. 1. Fundamental concepts. Philosophical Transactions of the Royal Society of London Series a-Mathematical and Physical Sciences, 240(822), 459-508.
Sato, Y. (1970). On the Second Order Approximation in the Phenomenological Theory of Large Elastic Deformation. Journal of Society of Material Science of Japan, 19, 322-325.
Sato, Y. (1978). Construction of a Hierarchy of Approximation of Elasticity Theory of Finite Deformation. Nihon Reoroji Gakkaishi (Journal Soc. Rheol. Japan), 6, 58-78.
Seibert, D. J., & Schoche, N. (2000). Direct comparison of some recent rubber elasticity models. Rubber chemistry and technology, 73(2), 366-384.
Sharma, S. (2003). Critical comparison of popular hyper-elastic material models in design of anti-vibration mounts for automotive industry through FEA. Constitutive Models for Rubber, 161-168.
Suchocki, C., & Jemioło, S. (2020). On finite element implementation of polyconvex incompressible hyperelasticity: theory, coding and applications. International Journal of Computational Methods, 17(08), 1950049.
Tabaddor, F. (1987). Rubber elasticity models for finite element analysis. Computers & Structures, 26(1-2), 33-40.
Treloar, L. R. G. (1944). Stress-strain data for vulcanized rubber under various types of deformation. Rubber Chemistry and Technology, 17(4), 813-825.
Tschoegl, N. W. ( 1971). Constitutive equations for elastomers. Journal of Polymer Science Part A-1: Polymer Chemistry, 9(7), 1959-1970.
Van der Hoff, B. M. E., & Buckler, E. J. (1967). Transient changes in topology and energy on extension of polybutadiene networks. Journal of Macromolecular Science—Chemistry, 1(4), 747-788.
Yeoh, O. H. (1990). Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber chemistry and technology, 63(5), 792-805.
Zahorski, S. (1959). A form of elastic potential for rubber-like materials. Archives of Mechanics, 5, 613-617.