Poisson比为1/2材料中球形空穴突变和球形空穴萌生的分岔问题研究

金明; 黄克服; 武际可

Poisson比为1/2材料中球形空穴突变和球形空穴萌生的分岔问题研究

北京大学力学与工程科学系, 北京 100871

基金项目: 国家自然科学基金;国家教委博士点基金;大连理工大学结构工程国家重点实验室基金

详细信息

作者简介:
金明(1963~ ),男,讲师,博士.

中图分类号: O322
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- 被引次数: 0
出版历程
- 收稿日期: 1998-01-14
- 修回日期: 1999-02-08
- 刊出日期: 1999-08-15

A Study of the Catastrophe and the Cavitation for a Spherical Cavity in Hooke’s Material with 1/2 Poisson’s Ratio

Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China

摘要

摘要: 研究Poisson比为1/2的Hooke材料中,空穴的突变和萌生现象.求解一个球对称几何非线性弹性力学的移动边界(moving boundary)问题,空穴为球形,远离空穴处为三向均匀拉伸应力状态,在当前构形上列控制方程；在当前构形边界上列边界条件.找到了这个自由边界问题的封闭解并得到空穴半径趋于零时的叉型分岔解.计算结果显示,在位移-载荷曲线上存在一个切分岔型分岔点(或鞍结点型分岔点、极值型分岔点),这个分岔点说明在外力作用下空穴会发生突变,即突然“长大”;当球腔半径趋于零时,这个切分岔转化为叉型分岔(或分枝型分岔),这个叉型分岔可以解释实心球中的空穴萌生现象.
- 移动边界 /
- 切分岔 /
- 叉型分岔 /
- 空穴萌生
Abstract: In this paper, the catastrophe of a spherical cavity and the cavitation of a spherical cavity for Hooke. s material with 1/2 Poisson's ratio are studied. A nonlinear problem, which is a moving boundary problem for the geometrically nonlinear elasticity in radial symmetric, was solved analytically. The governing equations were written on the deformed region or on the present configuration. And the conditions were described on moving boundary. A closed form solution was found. Furthermore, a bifurcation solution in closed form was given from the trivial homogeneous solution of a solid sphere. The results indicate that there is a tangent bifurcation on the displacement-load curve for a sphere with a cavity. On the tangent bifurcation point, the cavity grows up suddenly, which is a kind of catastrophe. And there is a pit chfork bifurcation on the displacement-load curve for a solid sphere. On the pitchfork bifurcation point, there is a cavitation in the solid sphere.
- moving boundary /
- tangent bifurcation /
- pitchfork bifurcation /
- cavitation

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参考文献(14)

[1]	Gent A N,Lindley P B.I nternal rupture of bonded rubber cylinders in tension[J].Proc R Soc Lond,1959,A249(1257):195~205.
[2]	Ball J M.Discontinuous equilibrium solutions and cavitation in nonlinear elasticity[J].Phil Trans R Soc Lond,1982,A306:557~611.
[3]	Horgan C O,Abeyaratne R.A bifurcation problem for a compressible nonlinearly elastic medium:growth of micro-void[J].J Elasticity,1986,16:189~200.
[4]	Carroll M M.Finite strain solutions in compressible isotropic elasticity[J].J Elasticity,1988,20:65~92.
[5]	Hao Tian-Hu.A theory of the appearance and growth of the micro-void[J].Int J Fractur e,1990,43:R51~R55.
[6]	Horgan C O.Void nucleation and growth for compressible nonlinearly elastic materials:an example[J].Int J Solids Str u ctur es,1992,29(3):279~291.
[7]	尚新春,程昌钧.超弹性材料中的球形空穴分叉[J].力学学报,1996,28(6):751~755.
[8]	Chou Wang M-S.Void nucleation and growth for a class of incompressible nonlinearly elastic materials[J].Int J Solids Structures,1989,25(11):1239~1254.
[9]	Horgan C O,Pence T J.Cavity formation at the center of a composite incompressible nonlinearly elastic sphere[J].Tran sactions of the ASM E Journal of Applied Mechanics,1989,56:302~308.
[10]	Polignone D A,Horgan C O.Effects of material anisotropy and inhomogeneity on cavitation for composite incompressible anisotropic nonlinearly elastic spheres[J].Int J Solids Structures,1993,30(24):3381~3416.
[11]	Hou Hang-sheng.A study of combined asymmetric and cavitated bifurcations in neo-Hookean material under symmetric deadloading[J].Journal of Applied Mechanics,1993,60(2):1~7.
[12]	Ertan N.Influence of compressibility and hardening on cavitation[J].J Engng Mech,1988,114:1231~1244.
[13]	金明.内压下弹性薄膜球的稳定性[J].力学与实践,1997,19(3):32~33.
[14]	武际可,苏先樾.弹性系统的稳定性[M].北京:科学出版社,1994.