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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（ｍｏｖｉｎｇｂｏｕｎｄａｒｙ）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
To study the mutation and germination of holes in a Hooke material with a Poisson’s ratio of ½, solve the problem of moving boundary of a spherical symmetric geometrically nonlinear elastic mechanics. The cavities are spherical and three-dimensionally far away from the cavities Tensile stress state, in the current configuration of the governing equations; in the boundary of the boundary conditions of the current configuration boundary · Find the closed boundary solution of this free boundary problem and the hole radius tends to zero fork-type solution · Calculation The results show that there exists a bifurcated bifurcation point (or saddle node bifurcation point and extreme bifurcation point) on the displacement-load curve. This bifurcation point indicates that the cavity will mutate under the external force , Which suddenly “grows up”. When the radius of the cavity tends to zero, this bifurcation transforms into a forked bifurcation (or branching bifurcation), which can explain the initiation of cavitation in a solid sphere phenomenon