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Transversely isotropic hyper-elastic material rectangular plate with voids under a uniaxial extension

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Abstract

The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper-elastic material with the generalized neo-Hookean strain energy function under a uniaxial extension are studied. The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations. The solution may be approximately obtained from the minimum potential energy principle. Thus, the analytic solutions of the deformation and stress of the plate are obtained. The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy, the size of the voids and the distance between the voids are discussed. The characteristics of the growth of the voids and the distribution of stresses of the plates with one void, Three or five voids are obtained and compared.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, P. R. China

    Cheng Chang-jun & Ren Jiu-sheng

  2. Department of Mechanics, Shanghai University, 200072, Shanghai, P. R. China

    Cheng Chang-jun & Ren Jiu-sheng

Authors
  1. Cheng Chang-jun
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  2. Ren Jiu-sheng
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Additional information

Contributed by CHENG Chang-jun

Foundation item: the National Natural Science Foundation of China (10272069)

Biography: CHENG Chang-jun (1937≈), Professor (E-mail: chjcheng@mail.shu.edu.cn)

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Chang-jun, C., Jiu-sheng, R. Transversely isotropic hyper-elastic material rectangular plate with voids under a uniaxial extension. Appl Math Mech 24, 763–773 (2003). https://doi.org/10.1007/BF02437808

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  • DOI: https://doi.org/10.1007/BF02437808

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