A model of incompressible isotropic hyperelastic material behavior using spline interpolations of tension-compression test data
We present a model of incompressible isotropic hyperelastic material behavior based on a strain energy description separable in terms of logarithmic strains and piecewise spline interpolations of uniaxial tension–compression test data. Valuable attributes are that no fitting of model constants is ca...
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| Published in | Communications in numerical methods in engineering Vol. 25; no. 1; pp. 53 - 63 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
01.01.2009
Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1069-8299 1099-0887 |
| DOI | 10.1002/cnm.1105 |
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| Abstract | We present a model of incompressible isotropic hyperelastic material behavior based on a strain energy description separable in terms of logarithmic strains and piecewise spline interpolations of uniaxial tension–compression test data. Valuable attributes are that no fitting of model constants is carried out and the model replicates even physically complicated test data very accurately for small and large strains and for tension and compression. The model is well suited for use in finite element analysis. Copyright © 2008 John Wiley & Sons, Ltd. |
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| AbstractList | We present a model of incompressible isotropic hyperelastic material behavior based on a strain energy description separable in terms of logarithmic strains and piecewise spline interpolations of uniaxial tension-compression test data. Valuable attributes are that no fitting of model constants is carried out and the model replicates even physically complicated test data very accurately for small and large strains and for tension and compression. The model is well suited for use in finite element analysis. We present a model of incompressible isotropic hyperelastic material behavior based on a strain energy description separable in terms of logarithmic strains and piecewise spline interpolations of uniaxial tension–compression test data. Valuable attributes are that no fitting of model constants is carried out and the model replicates even physically complicated test data very accurately for small and large strains and for tension and compression. The model is well suited for use in finite element analysis. Copyright © 2008 John Wiley & Sons, Ltd. |
| Author | Sussman, Theodore Bathe, Klaus-Jürgen |
| Author_xml | – sequence: 1 givenname: Theodore surname: Sussman fullname: Sussman, Theodore organization: ADINA R & D, Inc., Watertown, MA 02472, U.S.A – sequence: 2 givenname: Klaus-Jürgen surname: Bathe fullname: Bathe, Klaus-Jürgen email: kjb@mit.edu organization: Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A |
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| Cites_doi | 10.1088/0022-3727/8/11/007 10.1016/0955-7997(84)90049-3 10.1063/1.1712836 10.1122/1.549568 10.1063/1.1710039 10.1016/0045-7949(87)90265-3 10.5254/1.3547602 10.1063/1.1735971 10.1007/BF00789105 |
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| Keywords | High strain rubber-like materials Logarithmic function Strain energy Uniaxial tension stress Data compression Incompressible material finite element analysis Compression test Modeling Tension test Spline approximation Hyperelasticity Finite element method Uniaxial compression incompressible materials Model matching material modeling Rubber |
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| References | Mooney M. A theory of large elastic deformation. Journal of Applied Physics 1940; 2:582-592. Hamming RW. Numerical Methods for Scientists and Engineers. Dover: New York, 1973. Boyce MC, Arruda EM. Constitutive models of rubber elasticity: a review. Rubber Chemistry and Technology 2000; 73(3):504-523. Sussman T, Bathe KJ. A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Journal of Computers and Structures 1987; 26:357-409. Carmichael AJ, Holdaway HW. Phenomenological elastomechanical behavior of rubbers over wide ranges of strain. Journal of Applied Physics 1961; 32(2):159-166. Valanis KC, Landel RF. The strain-energy function of a hyperelastic material in terms of the extension ratios. Journal of Applied Physics 1967; 38(7):2997-3002. van den Bogert PAJ, de Borst R. On the behaviour of rubber-like materials in compression and shear. Archive of Applied Mechanics 1994; 64:136-146. Kearsley EA, Zapas LJ. Some methods of measurement of an elastic strain-energy function of the Valanis-Landel type. Journal of Rheology 1980; 24(4):483-500. Jones DF, Treloar LRG. The properties of rubber in pure homogeneous strain. Journal of Physics D: Applied Physics 1975; 8:1285-1304. Bathe KJ. Finite Element Procedures. Prentice-Hall: Englewood Cliffs, NJ, 1996. Ogden RW. Non-Linear Elastic Deformations. Ellis Horwood: Chichester, U.K., 1984. 1940; 2 2000; 73 1996 1984 1973 1961; 32 1967; 38 1975; 8 1980; 24 1987; 26 1994; 64 e_1_2_1_6_2 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_3_2 e_1_2_1_12_2 Bathe KJ (e_1_2_1_2_2) 1996 e_1_2_1_10_2 Hamming RW (e_1_2_1_11_2) 1973 e_1_2_1_8_2 e_1_2_1_9_2 |
| References_xml | – reference: Ogden RW. Non-Linear Elastic Deformations. Ellis Horwood: Chichester, U.K., 1984. – reference: Mooney M. A theory of large elastic deformation. Journal of Applied Physics 1940; 2:582-592. – reference: Sussman T, Bathe KJ. A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Journal of Computers and Structures 1987; 26:357-409. – reference: van den Bogert PAJ, de Borst R. On the behaviour of rubber-like materials in compression and shear. Archive of Applied Mechanics 1994; 64:136-146. – reference: Valanis KC, Landel RF. The strain-energy function of a hyperelastic material in terms of the extension ratios. Journal of Applied Physics 1967; 38(7):2997-3002. – reference: Carmichael AJ, Holdaway HW. Phenomenological elastomechanical behavior of rubbers over wide ranges of strain. Journal of Applied Physics 1961; 32(2):159-166. – reference: Bathe KJ. Finite Element Procedures. Prentice-Hall: Englewood Cliffs, NJ, 1996. – reference: Boyce MC, Arruda EM. Constitutive models of rubber elasticity: a review. Rubber Chemistry and Technology 2000; 73(3):504-523. – reference: Kearsley EA, Zapas LJ. Some methods of measurement of an elastic strain-energy function of the Valanis-Landel type. Journal of Rheology 1980; 24(4):483-500. – reference: Jones DF, Treloar LRG. The properties of rubber in pure homogeneous strain. Journal of Physics D: Applied Physics 1975; 8:1285-1304. – reference: Hamming RW. Numerical Methods for Scientists and Engineers. Dover: New York, 1973. – volume: 38 start-page: 2997 issue: 7 year: 1967 end-page: 3002 article-title: The strain‐energy function of a hyperelastic material in terms of the extension ratios publication-title: Journal of Applied Physics – year: 1973 – year: 1996 – volume: 32 start-page: 159 issue: 2 year: 1961 end-page: 166 article-title: Phenomenological elastomechanical behavior of rubbers over wide ranges of strain publication-title: Journal of Applied Physics – volume: 73 start-page: 504 issue: 3 year: 2000 end-page: 523 article-title: Constitutive models of rubber elasticity: a review publication-title: Rubber Chemistry and Technology – year: 1984 – volume: 8 start-page: 1285 year: 1975 end-page: 1304 article-title: The properties of rubber in pure homogeneous strain publication-title: Journal of Physics D: Applied Physics – volume: 2 start-page: 582 year: 1940 end-page: 592 article-title: A theory of large elastic deformation publication-title: Journal of Applied Physics – volume: 26 start-page: 357 year: 1987 end-page: 409 article-title: A finite element formulation for nonlinear incompressible elastic and inelastic analysis publication-title: Journal of Computers and Structures – volume: 64 start-page: 136 year: 1994 end-page: 146 article-title: On the behaviour of rubber‐like materials in compression and shear publication-title: Archive of Applied Mechanics – volume: 24 start-page: 483 issue: 4 year: 1980 end-page: 500 article-title: Some methods of measurement of an elastic strain‐energy function of the Valanis–Landel type publication-title: Journal of Rheology – ident: e_1_2_1_10_2 doi: 10.1088/0022-3727/8/11/007 – ident: e_1_2_1_9_2 doi: 10.1016/0955-7997(84)90049-3 – ident: e_1_2_1_5_2 doi: 10.1063/1.1712836 – ident: e_1_2_1_8_2 doi: 10.1122/1.549568 – ident: e_1_2_1_7_2 doi: 10.1063/1.1710039 – ident: e_1_2_1_12_2 doi: 10.1016/0045-7949(87)90265-3 – ident: e_1_2_1_3_2 doi: 10.5254/1.3547602 – ident: e_1_2_1_6_2 doi: 10.1063/1.1735971 – volume-title: Numerical Methods for Scientists and Engineers year: 1973 ident: e_1_2_1_11_2 – volume-title: Finite Element Procedures year: 1996 ident: e_1_2_1_2_2 – ident: e_1_2_1_4_2 doi: 10.1007/BF00789105 |
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| SubjectTerms | Applied sciences Computational techniques Elastomers Exact sciences and technology finite element analysis Fundamental areas of phenomenology (including applications) hyperelasticity incompressible materials Industrial polymers. Preparations material modeling Mathematical methods in physics Physics Polymer industry, paints, wood rubber-like materials Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Technology of polymers |
| Title | A model of incompressible isotropic hyperelastic material behavior using spline interpolations of tension-compression test data |
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