How to cite this paper
Franus, A., Jemioło, S & Antoni, M. (2020). A slightly compressible hyperelastic material model implementation in ABAQUS.Engineering Solid Mechanics, 8(4), 365-380.
Refrences
Alexander, H. (1968). A constitutive relation for rubber-like materials. International Journal of Engineering Science, 6(9), 549-563.
Ball, J. M. (1977). Convexity conditions and existence theorems in nonlinear elasticity. Archive for Rational Mechanics and Analysis 66, 63(4), 337-403.
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.
Brezzi, F., & Fortin, M. (1991). Mixed and Hybrid Finite Element Method. New York: Springer-Verlag.
Chadwick, P. (1974). Thermo-Mechanics of Rubberlike Materials. Philosophical Transactions of The Royal Society A, Mathematical Physical and Engineering Sciences, 276(1260), 371–403.
Ciarlet, P. G. (1988). Mathematical elasticity. Volume I: Three-dimensional elasticity. Amsterdam: North-Holland.
Dassault Systèmes. (2015). ABAQUS 2016 Analysis user’s guide. Volume III: Materials.
Dassault Systèmes. (2015). ABAQUS 2016 Theory Manual.
Doll, S., & Schweizerhof, K. (1999). On the development of volumetric strain energy function. J. Appl. Mech., 67(1), 17-21.
Ehlers, W., & Eipper, G. (1998). The simple tension problem at large volumetric strains computed from finite hyperelastic material laws. Acta Mechanica, 130(1-2), 17-27.
Franus, A., & Jemioło, S. (2019). Zastosowanie aproksymacji średniokwadratowej do wyznaczania parametrów wielomianowych modeli hipersprężystości [Application of least-squares approximation to determine the parameters of polynomial hyperelastic models]. In S. Jemioło (Ed.), Nieliniowa sprężystość. Modelowanie konstytutywne, stateczność i zagadnienia falowe. Warsaw: OWPW.
Holzapfel, G. A. (2010). Nonlinear solid mechanics. New York: John Wiley & Sons Ltd.
Isihara, A., Hashitsume, N., & Tatibana, M. (1951). Statistical Theory of Rubber‐Like Elasticity. IV. (Two‐Dimensional Stretching). The Journal of Chemical Physics, 19(1508), 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.
Jemioło, S. (2016). Relacje konstytutywne hipersprężystości [Constitutive relationships of hyperelasticity]. Warsaw: KILiW PAN.
Jemioło, S. (2019). Materiały małościśliwe – uogólnienia modelu MV [Slightly compressible materials – a generalisation of MV model]. In S. Jemioło (Ed.), Nieliniowa sprężystość. Modelowanie konstytutywne, stateczność i zagadnienia falowe. Warsaw: OWPW.
Jemioło, S., & Franus, A. (2018). Numerical implementation of the Murnaghan material model in ABAQUS/Standard. MATEC Web of Conferences. 196, p. 01042. EDP Sciences.
Jemioło, S., & Franus, A. (2019). Metodyka wyznaczania parametrów materiałowych modeli hipersprężytości o wielomianowej funkcji energii [Methodology for identification parameters of hyperelastic polynomial models]. In S. Jemioło (Ed.), Nieliniowa sprężystość. Modelowanie konstytutywne, stateczność i zagadnienia falowe. Warsaw: OWPW.
Levinson, M., & Burgess, I. W. (1971). A comparison of some simple constitutive relations for slightly compressible rubber-like materials. International Journal of Mechanical Sciences, 13(6), 563-572.
Mooney, M. (1940). A Theory of Large Elastic Deformation. Journal of Applied Physics, 11(582), pp. 582-592.
Ogden, R. W. (1984). Non-linear elastic deformations. New York: Dover Publication.
Rivlin, R. S. (1948). Large elastic deformations of isotropic materials. II Some uniqueness theorems for pure homogeneous deformation. 240(822), 491-508.
Suchocki, C. (2017). Finite element implementation of slightly compressible and incompressible first invariant-based hyperelasticity. 55(3), 797-800. doi:10.15632/jtam-pl.55.3.787
Suchocki, C., & Jemioło, S. (2019). On finite element implementation of polyconvex incompressible hyperelasticity. Theory, Coding and Applications. doi:https://doi.org/10.1142/S021987621950049X
Yeoh, O. H. (1990). Characterization of elastic properties of carbon black filled rubber vulcanizates. 63(5), 792-805.
Zahorski, S. (1959). A form of the elastic potential for rubber-like materials. 5, 613–618.
Zienkiewicz, O. C., Taylor, R. L., & Fox, D. (2014). The Finite Element Method for Solid and Structural Mechanics. Butterworth-Heinemann.
Ball, J. M. (1977). Convexity conditions and existence theorems in nonlinear elasticity. Archive for Rational Mechanics and Analysis 66, 63(4), 337-403.
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.
Brezzi, F., & Fortin, M. (1991). Mixed and Hybrid Finite Element Method. New York: Springer-Verlag.
Chadwick, P. (1974). Thermo-Mechanics of Rubberlike Materials. Philosophical Transactions of The Royal Society A, Mathematical Physical and Engineering Sciences, 276(1260), 371–403.
Ciarlet, P. G. (1988). Mathematical elasticity. Volume I: Three-dimensional elasticity. Amsterdam: North-Holland.
Dassault Systèmes. (2015). ABAQUS 2016 Analysis user’s guide. Volume III: Materials.
Dassault Systèmes. (2015). ABAQUS 2016 Theory Manual.
Doll, S., & Schweizerhof, K. (1999). On the development of volumetric strain energy function. J. Appl. Mech., 67(1), 17-21.
Ehlers, W., & Eipper, G. (1998). The simple tension problem at large volumetric strains computed from finite hyperelastic material laws. Acta Mechanica, 130(1-2), 17-27.
Franus, A., & Jemioło, S. (2019). Zastosowanie aproksymacji średniokwadratowej do wyznaczania parametrów wielomianowych modeli hipersprężystości [Application of least-squares approximation to determine the parameters of polynomial hyperelastic models]. In S. Jemioło (Ed.), Nieliniowa sprężystość. Modelowanie konstytutywne, stateczność i zagadnienia falowe. Warsaw: OWPW.
Holzapfel, G. A. (2010). Nonlinear solid mechanics. New York: John Wiley & Sons Ltd.
Isihara, A., Hashitsume, N., & Tatibana, M. (1951). Statistical Theory of Rubber‐Like Elasticity. IV. (Two‐Dimensional Stretching). The Journal of Chemical Physics, 19(1508), 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.
Jemioło, S. (2016). Relacje konstytutywne hipersprężystości [Constitutive relationships of hyperelasticity]. Warsaw: KILiW PAN.
Jemioło, S. (2019). Materiały małościśliwe – uogólnienia modelu MV [Slightly compressible materials – a generalisation of MV model]. In S. Jemioło (Ed.), Nieliniowa sprężystość. Modelowanie konstytutywne, stateczność i zagadnienia falowe. Warsaw: OWPW.
Jemioło, S., & Franus, A. (2018). Numerical implementation of the Murnaghan material model in ABAQUS/Standard. MATEC Web of Conferences. 196, p. 01042. EDP Sciences.
Jemioło, S., & Franus, A. (2019). Metodyka wyznaczania parametrów materiałowych modeli hipersprężytości o wielomianowej funkcji energii [Methodology for identification parameters of hyperelastic polynomial models]. In S. Jemioło (Ed.), Nieliniowa sprężystość. Modelowanie konstytutywne, stateczność i zagadnienia falowe. Warsaw: OWPW.
Levinson, M., & Burgess, I. W. (1971). A comparison of some simple constitutive relations for slightly compressible rubber-like materials. International Journal of Mechanical Sciences, 13(6), 563-572.
Mooney, M. (1940). A Theory of Large Elastic Deformation. Journal of Applied Physics, 11(582), pp. 582-592.
Ogden, R. W. (1984). Non-linear elastic deformations. New York: Dover Publication.
Rivlin, R. S. (1948). Large elastic deformations of isotropic materials. II Some uniqueness theorems for pure homogeneous deformation. 240(822), 491-508.
Suchocki, C. (2017). Finite element implementation of slightly compressible and incompressible first invariant-based hyperelasticity. 55(3), 797-800. doi:10.15632/jtam-pl.55.3.787
Suchocki, C., & Jemioło, S. (2019). On finite element implementation of polyconvex incompressible hyperelasticity. Theory, Coding and Applications. doi:https://doi.org/10.1142/S021987621950049X
Yeoh, O. H. (1990). Characterization of elastic properties of carbon black filled rubber vulcanizates. 63(5), 792-805.
Zahorski, S. (1959). A form of the elastic potential for rubber-like materials. 5, 613–618.
Zienkiewicz, O. C., Taylor, R. L., & Fox, D. (2014). The Finite Element Method for Solid and Structural Mechanics. Butterworth-Heinemann.