A tiny spherical cavity will expand unboundedly in a homogenous incompressible neo-Hookean solid when the applied hydrostatic tension reaches five times of the shear modulus of the solid. Such phenomenon is usually referred as cavitation in a soft solid. In the previous studies, the soft solid is often assumed to have homogeneous mechanical properties. In this paper, the effects of inhomogeneity have been investigated by assuming the shear modulus in the solid varies affinely with the radial coordinate. A bifurcation problem is considered for a graded neo-Hookean solid subjected to uniform hydrostatic tension on the external boundary. We find that the cavitation solution with a traction-free internal cavity can be analytically expressed using hypergeometric function. For large hydrostatic tension, the equilibrium configuration can bifurcate from the trivial solution (no cavity) to the cavitation solution (cavity occurs). Both the trivial solution and cavitation solution can be stable and unstable determined by minima of their potential energy. When the external hydrostatic tension is greater than a critical value, the internal cavity can expand both continuously or discontinuously inside the solid. We hope the results obtained in this article will be helpful to understand the cavitation phenomenon in complex soft materials.

当施加的静水压力达到固体剪切模量的五倍时，微小的球形空腔将在均质不可压缩的新霍克固体中无限扩展。这种现象通常称为软固体中的气蚀现象。在先前的研究中，通常假定软固体具有均一的机械性能。在本文中，通过假设固体中的剪切模量随径向坐标仿射变化来研究不均匀性的影响。对于在外边界上经受均匀静水压力的梯度新霍克固体，考虑了分叉问题。我们发现可以使用超几何函数解析地表达具有无牵引力内腔的空化溶液。对于较大的静液压，平衡构型可以从平凡的溶液（无空腔）分叉到空化溶液（发生空腔）。琐碎溶液和空化溶液都可以通过其势能的最小值来确定是稳定的还是不稳定的。当外部静水压力大于临界值时，内部空腔会在固体内部连续或不连续地膨胀。我们希望本文中获得的结果将有助于理解复杂软材料中的空化现象。内部空腔可以在固体内部连续或不连续地膨胀。我们希望本文中获得的结果将有助于理解复杂软材料中的空化现象。内部空腔可以在固体内部连续或不连续地膨胀。我们希望本文中获得的结果将有助于理解复杂软材料中的空化现象。