本文主要探討Neo-Hookean 材料圓球孔洞運動方程，其在外力作用下，孔洞的擴張情形。由於橡膠材料在工程領域範圍使用繁多，而我們知道橡膠材料的破壞開裂與與其裂縫尖端的孔洞有關，因此本文研究孔洞擴張的行為可供設計者作為參考的依據。橡膠材料在製造的過程中可能由於些許氣泡的產生尚未排出就定型於橡膠材料裡，所以本文主要探討Neo-Hookean材料圓球模型內孔洞在有壓力的作用下與外加週期荷重時的交互作用情形。

In this paper, a response of solid sphere composed of neo-hookean material which has a micro-void in the center is studied. Because there are many applications of rubber material in the engineering field, and we also know that if there is a micro-void embedded in the material, when the material is subjected to some kind of tensile loadings, the void will grow up, and finally when the loading reach to an critical value, the material will fail. So the critical value will be a reference for the designer.
In the process of manufacture rubber material, there may be some kind of air stay inside of the material, so in the analysis we put a pressure in the void, and the outer surface of the solid sphere is subjected to a harmonic load simultaneously. We will focus on the interaction of the outer loading and inside pressure and find the critical value of the loading.

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