不可压缩球体空穴的动态生成和分叉

利用Gao Y C给出的一类应变能函数,在有限变形动力学的框架内分析了不可压缩均匀球体突受拉伸恒载作用时空穴的动态生成和分叉问题.给出了存在动态分叉解的条件,确定了外载荷与空穴半径的解析关系,得到了临界载荷的表达式、空穴动态生成后应力分布的解析解、空穴半径振动的相图以及近似振动周期.讨论了本构参数对临界载荷、外载荷与最大振幅的关系的影响.结果表明:动态模型可以方便地退化为静态模型;当外加载荷大于临界载荷时,球体中心处存在一个突然生成并能迅速增大的空穴,且空穴半径随着时间的演化是周期性的非线性振动.

Dynamic formation and bifurcation of cavitation in an incompressible sphere

With the help of the strain energy function proposed by Y.C.Gao,dynamic formation and bifurcation of cavities in a homogeneous incompressible solid sphere subjected to a suddenly applied uniform tensile dead-loading was investigated with the theory of finite deformation dynamics.The conditions under which a solution for dynamic bifurcation existed were given.The relationship between the external load and the cavity radius was determined.The expressions of the critical load,the analytic solution of the stress distribution after the cavity being formed,the oscillation phase diagram of the cavity radius and the approximate oscillation period were also obtained.Finally,the influences of constitutive parameter on the critical load and the relationship between the load and the maximum amplitude were obtained as well.The results indicated that the dynamic model can be conveniently degenerated to a static model;when the external load is larger than the critical load,a cavity suddenly occurs at the center of the sphere and grows up quickly,in addition the growth of the radius of cavity shows a periodic nonlinear oscillation.