Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (1): 13-24.doi: https://doi.org/10.1007/s10483-014-1768-x

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Further study of rubber-like elasticity: elastic potentials matching biaxial data

章宇雨 李浩 肖衡   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China
  • 收稿日期:2013-03-14 修回日期:2013-08-22 出版日期:2014-01-20 发布日期:2013-12-27

Further study of rubber-like elasticity: elastic potentials matching biaxial data

 ZHANG Yu-Yu, LI Hao, XIAO Heng   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China
  • Received:2013-03-14 Revised:2013-08-22 Online:2014-01-20 Published:2013-12-27

摘要:

By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduces the determination of multiaxial elastic potentials to that of two one-dimensional potentials, thus bypassing usual cumbersome procedures of identifying a number of unknown parameters. Predictions of the suggested potential are derived for a general biaxial stretch test and compared with the classical data given by Rivlin and Saunders (Rivlin, R. S. and Saunders, D. W. Large elastic deformation of isotropic materials. VII: experiments on the deformation of rubber. Phill. Trans. Royal Soc. London A, 243, 251–288 (1951)). Good agreement is achieved with these extensive data.

关键词: elastic potential, logarithmic strain, elastomer, rational interpolation, biaxial stretch

Abstract:

By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduces the determination of multiaxial elastic potentials to that of two one-dimensional potentials, thus bypassing usual cumbersome procedures of identifying a number of unknown parameters. Predictions of the suggested potential are derived for a general biaxial stretch test and compared with the classical data given by Rivlin and Saunders (Rivlin, R. S. and Saunders, D. W. Large elastic deformation of isotropic materials. VII: experiments on the deformation of rubber. Phill. Trans. Royal Soc. London A, 243, 251–288 (1951)). Good agreement is achieved with these extensive data.

Key words: sensitive dimension, Duffings equation, sub-harmonic, transient process, fractal characteristic, rational interpolation, elastomer, biaxial stretch, elastic potential, logarithmic strain

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