A phenomenological constitutive model for predicting both the moderate and large deformation behavior of elastomeric materials

Mechanics of Materials - Tập 165 - Trang 104179 - 2022
Stephen Kirwa Melly1, Liwu Liu1, Yanju Liu1, Jinsong Leng2
1Department of Astronautical Science and Mechanics, Harbin Institute of Technology (HIT), P.O. Box 301, No. 92 West Dazhi Street, Harbin, 150001, PR China
2Center for Composite Materials and Structures, Harbin Institute of Technology (HIT), P.O. Box 3011, No. 2 Yikuang Street, Harbin, 150080, PR China

Tài liệu tham khảo

Alexander, 1968, A constitutive relation for rubber-like materials, Int. J. Eng. Sci., 6, 549, 10.1016/0020-7225(68)90006-2 Anssari-Benam, 2021, A generalised neo-Hookean strain energy function for application to the finite deformation of elastomers, Int. J. Non Lin. Mech., 128, 103626, 10.1016/j.ijnonlinmec.2020.103626 Anssari-Benam, 2021, On the central role of the invariant I2 in nonlinear elasticity, Int. J. Eng. Sci., 163, 103486, 10.1016/j.ijengsci.2021.103486 Arruda, 1993, A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, J. Mech. Phys. Solid., 4, 389, 10.1016/0022-5096(93)90013-6 Bahreman, 2016, Constitutive modeling of isotropic hyperelastic materials using proposed phenomenological models in terms of strain invariants, Polym. Eng. Sci., 56, 299, 10.1002/pen.24255 Bergström, 2015 Betchewe, 2020, A phenomenological expression of strain energy in large elastic deformations of isotropic materials, Iran. Polym. J. (Engl. Ed.), 29, 525, 10.1007/s13726-020-00816-6 Biderman, 1958, Calculation of rubber parts (in Russian), Rascheti na prochnost, 40 Bischoff, 2001, A new constitutive model for the compressibility of elastomers at finite deformations, Rubber Chem. Technol., 74, 541, 10.5254/1.3544956 Carroll, 2011, A strain energy function for vulcanized rubbers, J. Elasticity, 103, 173, 10.1007/s10659-010-9279-0 Dal, 2021 Destrade, 2017, Methodical fitting for mathematical models of rubber-like materials, Proc. R. Soc. A., 473, 20160811, 10.1098/rspa.2016.0811 Doll, 2000, On the development of volumetric strain energy functions, J. Appl. Mech., 67, 17, 10.1115/1.321146 Francisco Lalo, 2019, Numerical modeling and experimental characterization of elastomeric pads bonded in a conical spring under multiaxial loads and pre-compression, 5182629 Gent, 1958, Forms for the stored (strain) energy function for vulcanized rubber, J. Polym. Sci., 28, 625, 10.1002/pol.1958.1202811814 Gornet, 2012, A new isotropic hyperelastic strain energy function in terms of invariants and its derivation into a pseudo-elastic model for Mullins effect: application to finite element analysis, 265 Horgan, 2007, Constitutive models for almost incompressible isotropic elastic rubber-like materials, J. Elasticity, 87, 133, 10.1007/s10659-007-9100-x Horgan, 2009, On the volumetric part of strain-energy functions used in the constitutive modeling of slightly compressible solid rubbers, Int. J. Solid Struct., 46, 3078, 10.1016/j.ijsolstr.2009.04.007 Kaliske, 1999, An extended tube-model for rubber elasticity: statistical-mechanical theory and finite element implementation, Rubber Chem. Technol., 72, 602, 10.5254/1.3538822 Kawabata, 1981, Experimental survey of the strain energy density function of isoprene rubber vulcanizate, Macromolecules, 14, 154, 10.1021/ma50002a032 Khajehsaeid, 2013, A hyperelastic constitutive model for rubber-like materials, Eur. J. Mech. Solid., 38, 144, 10.1016/j.euromechsol.2012.09.010 Levenberg, 1944, A method for the solution of certain non-linear problems in least squares, Q. Appl. Math., 2, 164, 10.1090/qam/10666 Melly, 2021, Improved Carroll's hyperelastic model considering compressibility and its finite element implementation, Acta Mech. Sin., 10.1007/s10409-021-01064-4 Marquardt, 1963, An algorithm for least-squares estimation of nonlinear parameters, J. Soc. Ind. Appl. Math., 11, 431, 10.1137/0111030 Mooney, 1940, A theory of large elastic deformation, J. Appl. Phys., 11, 582, 10.1063/1.1712836 Muhr, 2005, Modeling the stress-strain behavior of rubber, Rubber Chem. Technol., 78, 391, 10.5254/1.3547890 Murphy, 2018, Modelling slight compressibility for hyperelastic anisotropic materials, J. Elasticity, 131, 171, 10.1007/s10659-017-9650-5 Paul, 2012, Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar's data, Arch. Appl. Mech., 82, 1183, 10.1007/s00419-012-0610-z Ogden, 1972, Large deformation isotropic elasticity — on the correlation of theory and experiment for incompressible rubberlike solids, Proc. R. Soc. Lond. A, 326, 565, 10.1098/rspa.1972.0026 Rivlin, 1948, Large elastic deformations of isotropic materials. IV. Further developments of the general theory, Phil. Trans. Roy. Soc. Lond., 241, 379, 10.1098/rsta.1948.0024 Rivlin, 1951, Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber, Phil. Trans. Roy. Soc. Lond. Math. Phys. Sci., 243, 251, 10.1098/rsta.1951.0004 Treloar, 1944, Stress-strain data for vulcanized rubber under various types of deformation, Rubber Chem. Technol., 17, 813, 10.5254/1.3546701 Treloar, 1975 Upadhyay, 2019, Thermodynamics-based stability criteria for constitutive equations of isotropic hyperelastic solids, J. Mech. Phys. Solid., 124, 115, 10.1016/j.jmps.2018.09.038 Upadhyay, 2020, Hyperelastic constitutive modeling of hydrogels based on primary deformation modes and validation under 3D stress states, Int. J. Eng. Sci., 103314, 154 Upadhyay, 2020, Visco-hyperelastic constitutive modeling of strain rate sensitive soft materials, J. Mech. Phys. Solid., 135, 103777, 10.1016/j.jmps.2019.103777 Xiang, 2018, A general constitutive model of soft elastomers, J. Mech. Phys. Solid., 117, 110, 10.1016/j.jmps.2018.04.016 Yeoh, 1993, Some forms of the strain energy function for rubber, Rubber Chem. Technol., 66, 754, 10.5254/1.3538343