Acta Mechanica Solida Sinica

, Volume 25, Issue 3, pp 312–320 | Cite as

Coupling Effects of Void Shape and Void Size on the Growth of an Elliptic Void in a Fiber-Reinforced Hyper-Elastic Thin Plate

  • Jiusheng Ren
  • Hanhai Li
  • Changjun Cheng
  • Xuegang Yuan


The growth of a prolate or oblate elliptic micro-void in a fiber reinforced anisotropic incompressible hyper-elastic rectangular thin plate subjected to uniaxial extensions is studied within the framework of finite elasticity. Coupling effects of void shape and void size on the growth of the void are paid special attention to. The deformation function of the plate with an isolated elliptic void is given, which is expressed by two parameters to solve the differential equation. The solution is approximately obtained from the minimum potential energy principle. Deformation curves for the void with a wide range of void aspect ratios and the stress distributions on the surface of the void have been obtained by numerical computation. The growth behavior of the void and the characteristics of stress distributions on the surface of the void are captured. The combined effects of void size and void shape on the growth of the void in the thin plate are discussed. The maximum stresses for the void with different sizes and different void aspect ratios are compared.

Key words

fiber reinforced hyper-elastic material rectangular thin plate with void void shape and void size potential energy principle growth of void 


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  1. [1]
    Horgan, C.O. and Polignone, D.A., Cavitation in nonlinearly elastic solids: A review. Applied Mechanics Review, 1995, 48: 471–485.CrossRefGoogle Scholar
  2. [2]
    Fu, Y.B. and Ogden, R.W., Nonlinear Elasticity. Cambridge: Cambridge University Press, 2001.CrossRefGoogle Scholar
  3. [3]
    Gent, A.N., Elastic instabilities in rubber. International Journal of Nonlinear Mechanics, 2005, 40: 165–175.CrossRefGoogle Scholar
  4. [4]
    Horgan, C.O., Void nucleation and growth for compressible non-linearly elastic materials: An example. International Journal of Solids and Structures, 1992, 2: 279–291.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Oscar, L.P., Cavitation in compressible isotropic hyperelastic solids. Journal of Elasticity, 2009, 94: 115–145.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Cheng, C.J. and Shang, X.C., The growth of the voids in hyper-elastic rectangular plate under a uniaxial extension. Applied Mathematics and Mechanics, 1997, 18: 615–621.CrossRefGoogle Scholar
  7. [7]
    Zhang, J.P. and Batra, R.C., On the interaction between two circular voids in a nonlinear elastic solids. Acta Mechanica, 1994, 105: 161–171.CrossRefGoogle Scholar
  8. [8]
    Cheng, C.J. and Ren, J.S., Transversely isotropic hyper-elastic material rectangular plate with voids under a uniaxial extension. Applied Mathematics and Mechanics, 2003, 24: 763–773.CrossRefGoogle Scholar
  9. [9]
    Gent, A.N., Engineering with Rubber-How to Design Rubber Components. Munich: Carl Hanser Verlag, 2001.Google Scholar
  10. [10]
    Holzapfel, G.A., Gasser, T.C. and Ogden, R.W., A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity, 2000, 61: 1–48.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Marvalova, B. and Urban, R., Identification of orthotropic hyper-elastic material properties of card-rubber cylindrical air-spring. In:Experimental Stress Analysis of the 39th International Conference, 2001.Google Scholar
  12. [12]
    Merodio, J. and Ogden, R.W., The influence of the invariant I8 on the stress-deformation and ellipticity characteristics of doubly fiber-reinforced nonlinearly elastic solids. International Journal of Nonlinear Mechanics, 2006, 41: 556–563.CrossRefGoogle Scholar
  13. [13]
    Li, Z.H. and Huang, M.S., Combined effects of void shape and void size-oblate spheriodal microvoid embedded in infinite non-linear solid. International Journal of Plasticity, 2005, 21: 635–661.zbMATHGoogle Scholar
  14. [14]
    Li, Z.H. and Steinmann, P., RVE-based studies on the coupled effects of void size and void shape on yield behavior and void growth at micron scales. International Journal of Plasticity, 2006, 22: 1195–1216.CrossRefGoogle Scholar
  15. [15]
    Hou, H.S. and Abeyaratne, R., Cavitation in elastic and elastic-plastic solids. Journal of Mechanics Physics Solids, 1992, 3: 571–592.MathSciNetzbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2012

Authors and Affiliations

  • Jiusheng Ren
    • 1
    • 2
  • Hanhai Li
    • 1
  • Changjun Cheng
    • 1
    • 2
  • Xuegang Yuan
    • 3
  1. 1.Department of MechanicsShanghai UniversityShanghaiChina
  2. 2.Shanghai Key Laboratory of Mechanics in Energy and Environment EngineeringShanghaiChina
  3. 3.College of ScienceDalian Nationalities UniversityDalianChina

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