The cavitation of solid elastic spheres is a classical problem of continuum mechanics. Here, we study this problem within the context of "stochastic elasticity" where the constitutive parameters are characterised by probability density functions. We consider homogeneous spheres of stochastic neo-Hookean material, composites with two concentric stochastic neo-Hookean phases, and inhomogeneous spheres of locally neo-Hookean material with a radially varying parameter. In all cases, we show that the material at the centre determines the critical load at which a spherical cavity forms there. However, while under dead-load traction, a supercritical bifurcation, with stable cavitation, is obtained in a static sphere of stochastic neo-Hookean material, for the composite and radially inhomogeneous spheres, a subcritical bifurcation, with snap cavitation, is also possible. For the dynamic spheres, oscillatory motions are produced under suitable dead-load traction, such that a cavity forms and expands to a maximum radius, then collapses again to zero periodically, but not under impulse traction. Under a surface impulse, a subcritical bifurcation is found in a static sphere of stochastic neo-Hookean material and also in an inhomogeneous sphere, whereas in composite spheres, supercritical bifurcations can occur as well. Given the non-deterministic material parameters, the results can be characterised in terms of probability distributions.

中文翻译：

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随机弹性球体可能的空化和径向运动

固体弹性球的空化是连续介质力学的经典问题。在这里，我们在“随机弹性”的背景下研究这个问题，其中本构参数由概率密度函数表征。我们考虑随机新胡克材料的均匀球体，具有两个同心随机新胡克相的复合材料，以及具有径向变化参数的局部新胡克材料的非均匀球体。在所有情况下，我们表明中心的材料决定了在那里形成球形腔的临界载荷。然而，在恒载牵引下，在随机新胡克材料的静态球体中获得具有稳定空化的超临界分叉，对于复合球和径向非均匀球，亚临界分叉，带有快速空化，也是可能的。对于动态球体，在合适的恒载牵引下会产生振荡运动，从而形成一个空腔并扩大到最大半径，然后周期性地再次坍塌至零，但在脉冲牵引下不会。在表面脉冲下，在随机新胡克材料的静态球体和非均匀球体中发现亚临界分岔，而在复合球体中，也可能发生超临界分岔。给定非确定性材料参数，结果可以用概率分布来表征。但不是在脉冲牵引下。在表面脉冲下，在随机新胡克材料的静态球体和非均匀球体中发现亚临界分岔，而在复合球体中，也可能发生超临界分岔。给定非确定性材料参数，结果可以用概率分布来表征。但不是在脉冲牵引下。在表面脉冲下，在随机新胡克材料的静态球体和非均匀球体中发现亚临界分岔，而在复合球体中，也可能发生超临界分岔。给定非确定性材料参数，结果可以用概率分布来表征。