Dynamic cavitations in incompressible hyperelastic pre-strained circular sheets  

作　　者：YUAN XueGang ZHANG HongWu ZHANG WenZheng ZHAO Wei Dong Bin 

机构地区：[1]School of Science, Dalian Nationalities University, Dalian 116600, China [2]State Key Laboratory of Structural Analysis for Industrial Equipment Departmnt of Engineering Mecha Tics Techology, Dalian 116024, China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2011年第2期303-309,共7页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos.10872045, 10721062);the Program for New Century Excellent Talents in University (Grant No.NCET-09-0096);the Fundamental Research Funds for Central Universities (Grant No.DC10030104)

摘　　要：A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value;dynamically,it is proved that the formed cavity will present a nonlinearly periodic oscillation,which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere.Numerical simulations show the effects of prescribed radial tension,material parameter and tensile load on critical ten-sile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value; dynamically,it is proved that the formed cavity will present a nonlinearly periodic oscillation,which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere.Numerical simulations show the effects of prescribed radial tension,material parameter and tensile load on critical ten-sile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.

关 键 词：dynamic cavitation incompressible hyperelastic material pre-strained circular sheet nonlinearly periodic oscillation 

分 类 号：O357.1[理学—流体力学] O347.41[理学—力学]