DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (11): 1220-1227.

DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE

任九生, 程昌钧

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

收稿日期:2003-02-20 修回日期:2004-05-28 出版日期:2004-11-18 发布日期:2004-11-18
通讯作者: CHENG Chang-jun(Corresponding author, Tel:+86-21-56331454;Tel/Fax:+86-21-56380560;E-mail:chjcheng@mail.shu.edu.cn) E-mail:chjcheng@mail.shu.edu.cn
基金资助:
the National Natural Science Foundation of China(10272069);the Municipal Key Subject Programs of Shanghai

DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE

REN Jiu-sheng, CHENG Chang-jun

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

Received:2003-02-20 Revised:2004-05-28 Online:2004-11-18 Published:2004-11-18

摘要/Abstract

摘要： The dynamical formation of cavity in a hyper-elastic sphere composed of two materials with the incompressible strain energy function, subjected to a suddenly applied uniform radial tensile boundary dead-load, was studied following the theory of finite deformation dynamics. Besides a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the sphere when the tensile load is larger than its critical value. An exact differential relation between the cavity radius and the tensile land was obtained. It is proved that the evolution of cavity radius with time displays nonlinear periodic oscillations. The phase diagram for oscillation, the maximum amplitude, the approximate period and the critical load were all discussed.

Abstract: The dynamical formation of cavity in a hyper-elastic sphere composed of two materials with the incompressible strain energy function, subjected to a suddenly applied uniform radial tensile boundary dead-load, was studied following the theory of finite deformation dynamics. Besides a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the sphere when the tensile load is larger than its critical value. An exact differential relation between the cavity radius and the tensile land was obtained. It is proved that the evolution of cavity radius with time displays nonlinear periodic oscillations. The phase diagram for oscillation, the maximum amplitude, the approximate period and the critical load were all discussed.

中图分类号:

O343

任九生;程昌钧. DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(11): 1220-1227.

REN Jiu-sheng;CHENG Chang-jun. DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(11): 1220-1227.

参考文献

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DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE

DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE

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