Likely cavitation and radial motion of stochastic elastic spheres
Likely cavitation and radial motion of stochastic elastic spheres
复制标题
DOI：
10.1088/1361-6544/ab7104
复制
发表时间：
2019-06
期刊：
影响因子：
1.7
通讯作者：
L. Angela Mihai;T. Woolley;A. Goriely
中科院分区：
文献类型：
--
作者：
L. Angela Mihai;T. Woolley;A. Goriely
固体弹性球的空泡问题是连续介质力学的经典问题。在这里，我们研究这个问题的背景下，“随机弹性”的本构参数的特征在于概率密度函数。我们认为均匀球的随机neo-Hookean材料，复合材料与两个同心随机neo-Hookean阶段，和非均匀球的局部neo-Hookean材料与径向变化的参数。在所有情况下，我们表明，在中心的材料决定的临界载荷，在那里形成一个球形空腔。然而，而在静载牵引下，超临界分岔，稳定空化，随机neo-Hookean材料的静态球体中获得的复合材料和径向不均匀的球体，亚临界分岔，突然空化，也是可能的。对于动态球体，在适当的静载荷牵引下产生振荡运动，使得空腔形成并膨胀到最大半径，然后周期性地再次塌陷到零，但在脉冲牵引下不发生振荡运动。在表面脉冲作用下，在随机neo-Hookean材料的静态球体和非均匀球体中发现了亚临界分岔，而在复合球体中也可以发生超临界分岔。考虑到非确定性材料参数，结果可以用概率分布来表征。
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.