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Obtaining multi-axial elastic potentials for rubber-like materials via an explicit, exact approach based on spline interpolation

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Abstract

An explicit, exact approach is proposed to obtain multi-axial elastic potentials for isotropic rubber-like materials undergoing large incompressible deformations. By means of two direct, explicit procedures, this approach reduces the problem of determining multi-axial potentials to that of determining one-dimensional elastic potentials. To this end, two one-dimensional potentials for uniaxial case and simple shear case are respectively determined via spline interpolation and, then, the two potentials are extended to generate a multi-axial elastic potential using a novel method based on certain logarithmic invariants. Eventually, each of the multi-axial potentials will exactly match the finite strain data from four benchmark tests.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics & Mechanics and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, 200072, Shanghai, China

    Hao Li, Yuyu Zhang, Xiaoming Wang, Zhengnan Yin & Heng Xiao

Authors
  1. Hao Li
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  2. Yuyu Zhang
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  3. Xiaoming Wang
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  4. Zhengnan Yin
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  5. Heng Xiao
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Corresponding author

Correspondence to Heng Xiao.

Additional information

Project supported by the fund for innovative research from Shanghai University (No. A10-0401-12-001) and the start-up fund from the 211-project of the Education Committee of China through Shanghai University (No. A15-B002-09-032).

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Li, H., Zhang, Y., Wang, X. et al. Obtaining multi-axial elastic potentials for rubber-like materials via an explicit, exact approach based on spline interpolation. Acta Mech. Solida Sin. 27, 441–453 (2014). https://doi.org/10.1016/S0894-9166(14)60052-5

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  • DOI: https://doi.org/10.1016/S0894-9166(14)60052-5

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