The Growth of the Void in a Hyperelastic Rectangular Plate under a Uniaxial Extension

Cheng Changjun; Shang Xinchun

Volume 18 Issue 7

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(7): 573-578

Cheng Changjun, Shang Xinchun. The Growth of the Void in a Hyperelastic Rectangular Plate under a Uniaxial Extension[J]. Applied Mathematics and Mechanics, 1997, 18(7): 573-578.

Citation:

Cheng Changjun, Shang Xinchun. The Growth of the Void in a Hyperelastic Rectangular Plate under a Uniaxial Extension[J]. Applied Mathematics and Mechanics, 1997, 18(7): 573-578.

Citation:

Cheng Changjun, Shang Xinchun. The Growth of the Void in a Hyperelastic Rectangular Plate under a Uniaxial Extension[J]. Applied Mathematics and Mechanics, 1997, 18(7): 573-578.

PDF( 375 KB)

The Growth of the Void in a Hyperelastic Rectangular Plate under a Uniaxial Extension

Cheng Changjun^1,2,
Shang Xinchun²

1.
Shanghai University, Shanghai 200072, P. R. China;
2.
Lanzhou University, Lanzhou 730000, P. R. China

Received Date: 1996-12-18
Publish Date: 1997-07-15

Abstract

Abstract

In the presenl paper, the finite deformation and stress analysis for a hyperelasticrectangular plate with a center void under a uniaxial extension is studied. In order toconsider the effect of the existence of the void on the deformation and stress of theplate, the problem is reduced to the deformation and stress analysis for a hyperelustic annular plate and its approximate solution is obtained from the minimum potential energy principle. The growth of the cavitation iS also nunterically computed and analysed.
- hyperelastic rectangular plate,
- finite deformation,
- growth of void,
- variational principle

FullText(HTML)

References(9)

References

[1]	J,M,Ball,Discontinuous equilibrum solution and cavitation in elasticity,Phil.Trans,Rod,Soc,London,A30(1982),557-610.
[2]	C,O,Horgan and J.J.Pence,Cavity for mation at the center of a composite imcompressible nonlinearly elastic sphere,J.Appl.Mech.,50(1989)302-308.
[3]	Hou Hangsheng,A study of combined asymmetric and cavitated bifurcation in Neo-Hookey material under symmetric dead loading,J,Appl.Mech.,60 (1993),1-7.
[4]	P,Podio-Guidugli,C.G.Vergarm and E,G.Yirga,Discontinuous energy minimizers in non-linear elastostatics; An example of J.Ball revisited,J.Elasticity,1(1986),75-96.
[5]	D,A,Pol ignone and C.O.Horgan,Effect of material anisotropy and inhomogencity on cavitation for composite imcompressible nonlinear elastic spheres,3(1993),3381-3416.
[6]	C,D,Horgan and R.Abeyaratue,A bifurcation problem for a compressible nonlinear elastic medium,growth of a micro-void,J.Elasticitb,1(1986),189-200.
[7]	D,M.Haughton,Cavitation in compressible elastic membrances,Int.J.Engng,Sci.,2(1990),163-168.
[8]	T.T,Oden,Finite Elements of Nonlinear Continua,McGraw-Hill,New York(1972).
[9]	R.T.Shield,Equilibira solution in finite elasticity,ASME J.Appd.Mech.,50th Anniversarv Issue(1983).

Relative Articles

[1]	WANG Xi-gang, FU Ming-fu. Fuzzy Elasto-Visco-Plasticity Analysis of Finite Deformation Based on the L-D Plastic Flow Rule[J]. Applied Mathematics and Mechanics, 2015, 36(2): 128-139. doi: 10.3879/j.issn.1000-0887.2015.02.002
[2]	ZHANG Shan-yuan, LIU Zhi-fang. Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2008, 29(7): 825-832.
[3]	LIU Zhi-fang, ZHANG Shan-yuan. Solitary Waves in Finite Deformation Elastic Circular Rod[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1255-1260.
[4]	JIANG Wu-gui, HUANG Ming-hui. Analysis of Simple Shear Endochronic Equations for Finite Plastic Deformation[J]. Applied Mathematics and Mechanics, 2005, 26(1): 77-82.
[5]	GUO Jian-gang, ZHOU Li-jun, ZHANG Shan-yuan. Geometrical Nonlinear Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2005, 26(5): 614-620.
[6]	LI Jing-jing, CHENG Chang-jun. Differential Quadrature Method for Bending of Orthotropic Plates With Finite Deformation and Transverse Shear Effects[J]. Applied Mathematics and Mechanics, 2004, 25(8): 801-808.
[7]	ZHANG Yun, HUANG Zhu-ping. Mechanical Behavior of Amorphous Polymers in Shear[J]. Applied Mathematics and Mechanics, 2004, 25(10): 997-1006.
[8]	ZHOU Zhe, QIN Ling-li, HUANG Wen-bin, WANG Hong-wei. Effective Stress and Strain in Finite Deformation[J]. Applied Mathematics and Mechanics, 2004, 25(5): 542-550.
[9]	CHEN Shu-yu, SHEN Cheng-kang, JIN Wu-gen. Study on Dynamic Constitutive Relations for Concrete With Finite Deformation[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1257-1263.
[10]	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.
[11]	Jiang Yaodong, An Liqian, Liu Yanhua, Chen Zhida. Deformation Analysis of Laser Spectra Based on S-R Decomposition Theorem[J]. Applied Mathematics and Mechanics, 1999, 20(11): 1107-1114.
[12]	Wu Xiangfa, Fan Tianyou, Liu Changhe. Path-Independent J-Integral and Its Dual Form in Elastic-Plastic Solids with Finite Deformation[J]. Applied Mathematics and Mechanics, 1999, 20(3): 301-304.
[13]	Song Yanqi, Chen Zhida. Variational Principles of Asymmetric Elasticity Theory of Finite Deformation[J]. Applied Mathematics and Mechanics, 1999, 20(11): 1115-1120.
[14]	Guo Xingming. The Existence of Solution to the Finite Elastodynamics With Mixed Boundary Conditions[J]. Applied Mathematics and Mechanics, 1998, 19(1): 27-34.
[15]	Chen Zhida. Inverse Asymptotic Solution Method for Finite Deformation Elasto-Plasticity[J]. Applied Mathematics and Mechanics, 1997, 18(11): 959-966.
[16]	Dai Tianmin. Dynamical Equations of Various Types for Finite Deformable Polar Elastic Media[J]. Applied Mathematics and Mechanics, 1997, 18(10): 861-865.
[17]	Gao Hang-shan, Zhang Ru-qing. The Random Variational Principle in Finite Deformation of Elasticity and Finite Element Method[J]. Applied Mathematics and Mechanics, 1994, 15(10): 855-862.
[18]	Cao Guang-zhong, Xu Zhi-hong. Surface Instability of Elastic Half Spaces with Hydrostatic Loading on Their Surfaces[J]. Applied Mathematics and Mechanics, 1992, 13(1): 89-102.
[19]	Zhao Ya-pu, Hsueh Dah-wei. The Dynamic Plastic Behavior of a Simply Supported Circular Plate in a Damping Medium with Finite-Deflections[J]. Applied Mathematics and Mechanics, 1991, 12(10): 871-878.
[20]	Wang Hu Wang, Tsun-kuei. A Donnell Type Theory for Finite Deflection of Stiffened Thin Conical Shells Composed of Composite Materials[J]. Applied Mathematics and Mechanics, 1990, 11(9): 805-816.