Transversely Isotropic Hyper-Elastic Material Rectangular Plate With Voids Under a Uniaxial Extension

CHENG Chang-jun; REN Jiu-sheng

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(7): 675-683

CHENG Chang-jun, REN Jiu-sheng. Transversely Isotropic Hyper-Elastic Material Rectangular Plate With Voids Under a Uniaxial Extension[J]. Applied Mathematics and Mechanics, 2003, 24(7): 675-683.

Citation:

CHENG Chang-jun, REN Jiu-sheng. Transversely Isotropic Hyper-Elastic Material Rectangular Plate With Voids Under a Uniaxial Extension[J]. Applied Mathematics and Mechanics, 2003, 24(7): 675-683.

Citation:

CHENG Chang-jun, REN Jiu-sheng. Transversely Isotropic Hyper-Elastic Material Rectangular Plate With Voids Under a Uniaxial Extension[J]. Applied Mathematics and Mechanics, 2003, 24(7): 675-683.

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Transversely Isotropic Hyper-Elastic Material Rectangular Plate With Voids Under a Uniaxial Extension

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

Received Date: 2001-10-19
Rev Recd Date: 2002-02-21
Publish Date: 2003-07-15

Abstract

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.
- transversely isotropic,
- hyper-elastic material,
- rectangular plate with voids,
- finite deformation,
- potential energy principle,
- growth of voids

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References(10)

References

[1]	Horgan C O,Polignone D A.Cavitation in nonlinear elastic solids:A review[J].Applied Mechanics Review,1995,48(8):471-485.
[2]	Chou-Wang M-S,Horgan C O.Void nuclearation and growth for a class of incompressible nonlinearly elastic materials[J].Int J Solids Structures,1989,25(11):1239-1254.
[3]	任九生,程昌钧.不可压超弹性材料中的空穴分叉[J].应用数学和力学,2002,23(8):783-789.
[4]	REN Jiu-sheng,CHENG Chang-jun.Bifurcation of cavitation solutions for incompressible transversely isotropic hyper-elastic materials[J].Journal of Engineering Mathematics,2002,44(3):245-257.
[5]	Horgan C O,Abeyaratne R.A bifurcation problem for a compressible nonlinearly elastic medium:growth of a micro-void[J].J Elasticity,1986,16(1):189-200.
[6]	Horgan C O.Void nucleation and growth for compressible nonlinearly elastic materials:an example[J].Int J Solids Structures,1992,29(2):279-291.
[7]	程昌钧,尚新春.超弹性矩形板单向拉伸时微孔的增长[J].应用数学和力学,1997,18(6):573-578.
[8]	REN Jiu-sheng,CHENG Chang-jun,SHANG Xin-chun.The growth of a void in a rubber rectangular plate under uniaxial extension[J].Journal of Shanghai University,2001,5(3):177-182.
[9]	任九生,程昌钧.多孔Mooney-Rivlin材料矩形板的单向拉伸[J].力学季刊,2002,23(3):347-353.
[10]	Polignone D A,Horgan C O.Cavitation for incompressible anisotropic nonlinearly elastic spheres[J].J Elasticity,1993,33(1):27-65.