DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE

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

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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

Abstract

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.

2010 MSC Number:

O343

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

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References

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DYNAMICAL FORMATION OF CAVITY IN A COMPOSED HYPER-ELASTIC SPHERE

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