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COUPLING EFFECTS OF VOID SHAPE AND VOID SIZE ON THE GROWTH OF AN ELLIPTIC VOID IN A FIBER-REINFORCED HYPER-ELASTIC THIN PLATE

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Acta Mechanica Solida Sinica 2012年第3期25卷 312-320页

作者： Jiusheng Ren Hanhai Li Changjun Cheng Xuegang Yuan Department of Mechanics Shanghai UniversityShanghai 200444China Shanghai Key Laboratory of Mechanics in energy and Environment Engineering Shanghai 200444China College of Science Dalian Nationalities UniversityDalian 116600China

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.

关键词： fiber reinforced hyper-elastic material rectangular thin plate with void void shapeand void size potential energy principle growth of void

Growth of Voids in a Hyperelastic Rectangular Plate

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Journal of Shanghai University(English Edition) 2005年第3期9卷 194-200页

作者：程昌钧任九生 Department of Mechanics College of Sciences Shanghai University Shanghai 200072 P.R. ChinaShanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P.R.China Department of Mechanics College of Sciences Shanghai University Shanghai 200072 P.R. China

The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an initial central circular-cylinder void becomes an elliptic-cylinder void, but an initial non-centeral circular-cylinder void becomes an elliptic-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concentration was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyzed.

关键词： hyperelastic rectangular plate finite deformation potential energy principle growth of voids stress concentration.

Growth of a Void in a Rubber Rectangular Plate under Uniaxial Extension

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Journal of Shanghai University(English Edition) 2001年第3期5卷 177-182页

作者： RENJiu－sheng SHANGXin－chun InstituteofAppliedMathematicsandMechanics andDepartmentofMechanicsShanghaiUniversityShanghai200072China DepartmentofMathematicsandMechanics UniversityofScienceandTechnologyBe

The finite deformation and stress analyses for a rectangular plate with a center void and made of rubber with the Yeoh elastic strain energy function under uniaxial extension were studied in this paper. An approximation solution was obtained from the minimum potential energy principle. The numerical results for the growth of the cavitation and stresses along the edge of the cavitation were discussed. In addition, the stress concentration phenomenon was considered.

关键词： rubber rectangular plate finite deformation Yeoh strain energy function potential energy principle growth of void