Explicit Form of Elastic Potentials Matching General Biaxial Test Data for Elastomers

LI Hao; ZHANG Yu-yu; XIAO Heng

doi:10.3879/j.issn.1000-0887.2013.05.005

Volume 34 Issue 5

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LI Hao, ZHANG Yu-yu, XIAO Heng. Explicit Form of Elastic Potentials Matching General Biaxial Test Data for Elastomers[J]. Applied Mathematics and Mechanics, 2013, 34(5): 470-479. doi: 10.3879/j.issn.1000-0887.2013.05.005

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Explicit Form of Elastic Potentials Matching General Biaxial Test Data for Elastomers

doi: 10.3879/j.issn.1000-0887.2013.05.005

Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,

Received Date: 2013-01-25
Rev Recd Date: 2013-04-10
Publish Date: 2013-05-15

Abstract

Abstract

A direct approach was proposed to construct elastic potentials that exactly match uniaxial data and shear data based on spline interpolation. Explicit expressions were presented toward bypassing complicated numerical procedures in identifying unknown parameters. Predictions for the two normal stresses of biaxial test were derived and compared with Rivlin and Saunders’ data in 1951. Good agreement was achieved.
- elastomers,
- elastic potential,
- logarithmic strain,
- spline interpolation,
- general biaxial test

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References(23)

References

[1]	Treloar L R G.The Physics of Rubber Elasticity [M]. Oxford: Oxford University Press, 1975.
[2]	Arruda E M, Boyce M C. A three-dimensional constitutive model for the large stretch behavour of rubber elastic materials[J].J Mech Phys Solids,1993,41(2):389-412.
[3]	Boyce M C. Direct comparison of the Gent and the ArrudaBoyce constitutive models of rubber elasticity[J].Rubber Chem Techn,1996,69(5): 781-785.
[4]	Boyce M C, Arruda E M. Constitutive models of rubber elasticity: a reriew[J].Rubber Chem Techn,2000,73(3): 504-523.
[5]	Treloar L R G, Riding G. A nongaussian theory for rubber in biaxial strain—I: mechanical properties[J].Proc R Soc Lond Ser A,1979,369(1737): 261-280.
[6]	Rivlin R S. Large elastic deformation of isotropic materials—Ⅰ，Ⅱ: fundamental concepts; some uniqueness theories for pure homogeneous deformations[J].Philos Trans Roy Soc Lond, Ser A,1948,240(822): 459-508.
[7]	Tschoegl N W. Constitutive equations for elastomers[J].J Appl Polymer Sc, A1,1971,9(7): 1959-1970.
[8]	James A G, Green A. Strain energy function of rubber—Ⅱ: the characterization of filled vulcanizates[J]. J Appl Polymer Sci,1975,19(8): 2319-2330.
[9]	Morman Jr K N, Pan T Y. Application of finiteelement analysis in the design of automotive elastomeric components[J].Rubber Chemistry And Technology,1988,61(3): 503-533.
[10]	Gent A N. A new constitutive relation for rubber[J].Rubber Chemistry and Technology,1996,〖STHZ〗 69(1): 59-61.
[11]	Ogden R W. Large deformation isotropic elasticityon the correlation of theory and experiment for incompressible rubberlike materials[J].Proc Roy Soc London A,1972,326(1567): 565-584.
[12]	Ogden R W.NonLinear Elastic Deformations [M]. Chichester: Ellis Horwood, 1984.
[13]	李晓芳，杨晓翔.橡胶材料的超弹性本构模型[J]. 弹性体, 2005,15(1): 50-58. (LI Xiao-fang, YANG Xiao-xiang. A review of elastic constitutive model for rubber materials[J].China Elastomerics,2005,15(1): 50-58.(in Chinese))
[14]	Xiao H. An explicit, direct approach to obtaining multi-axial elastic potentials which exactly match data of four benchmark tests for incompressible rubberlike materials—part 1: incompressible deformations[J].Acta Mechanica,2012,223(9): 2039-2063.
[15]	Xiao H. An explicit, direct approach to obtain multi-axial elastic potentials which accurately match data of four benchmark tests for rubbery materials—part 2: general deformations[J].Acta Mechanica,2013,224(3):479-498.
[16]	Rivlin R S, Saunders D W. Large elastic deformations of isotropic materials—VII: experiments on the deformation of rubber[J].Phil Trans R Soc Lond A,1951,243(865): 251-288.
[17]	Xiao H. Hencky strain and Hencky model: extending history and ongoing tradition[J].Multidiscipline Modeling in Materials and Structures,2005,1(1):1-52.
[18]	Xiao H, Bruhns O T, Meyers A. Logarithmic strain, logarithmic spin and logarithmic rate[J].Acta Mechanica,1997,124(1/4): 89-105.
[19]	Xiao H, Bruhns O T, Meyers A. Hypoelasticity model based upon the logarithmic stress rate[J].J Elasticity,1997,47(1): 51-68.
[20]	Xiao H, Bruhns O T, Meyers A. The choice of objective rates in finite elastoplasticity: general results on the uniqueness of the logarithmic rate[J].Proc Roy Soc London A,2000,456(2000): 1865-1882.
[21]	Xiao H, Bruhns O T, Meyers A. Basic issues concerning finite strain measures and isotropic stress-deformation relations[J]. J Elasticity,2002,67(1): 1-23.
[22]	Xiao H, Bruhns O T, Meyers A. Explicit dual stressstrain and strain-stress relations of incompressible isotropic hyperelastic solids via deviatoric Hencky strain and Cauchy stress[J]. Acta Mechanica,2004,168(1/2): 21-33.
[23]	Xiao H, Chen L S. Hencky’s logarithmic strain measure and dual stressstrain and strainstress relations in isotropic finite hyperelasticity[J]. Int J Solids & Structures,2003,40(6): 1455-1463.