Likely Cavitation in Stochastic Elasticity
Likely Cavitation in Stochastic Elasticity
复制标题
随机弹性中可能出现空化
DOI：
10.1007/s10659-018-9706-1
复制
发表时间：
2018
影响因子：
2
通讯作者：
A. Goriely
中科院分区：
文献类型：
--
作者：
L. A. Mihai;Danielle Fitt;Thomas E. Woolley;A. Goriely
我们重新审视经典问题的弹性空化随机弹性的框架内。对于确定性弹性问题，涉及均匀各向同性不可压缩超弹性球径向对称张力下，有一个临界的静载牵引力，在该位置处，空穴可以发生某些材料。除了著名的情况下，稳定的空化后分叉的临界恒载，我们表明存在不稳定的突变空化满足Baker-Ericksen不等式的一些各向同性材料。对于随机问题，我们导出了分叉后变形的概率分布。在这种情况下，我们发现，由于材料参数的概率性质，总是有一个稳定和不稳定的状态之间的竞争。因此，在临界载荷下，以给定的概率发生稳定或不稳定的空化，并且还存在在比预期临界值更小或更大的载荷下可能形成空腔的概率。我们把这些现象称为“可能的空化”。此外，我们提供了均匀各向同性不可压缩材料的例子，表现出稳定或不稳定的空化与他们的随机等价物。
We revisit the classic problem of elastic cavitation within the framework of stochastic elasticity. For the deterministic elastic problem, involving homogeneous isotropic incompressible hyperelastic spheres under radially symmetric tension, there is a critical dead-load traction at which cavitation can occur for some materials. In addition to the well-known case of stable cavitation post-bifurcation at the critical dead load, we show the existence of unstable snap cavitation for some isotropic materials satisfying Baker-Ericksen inequalities. For the stochastic problem, we derive the probability distribution of the deformations after bifurcation. In this case, we find that, due to the probabilistic nature of the material parameters, there is always a competition between the stable and unstable states. Therefore, at a critical load, stable or unstable cavitation occurs with a given probability, and there is also a probability that the cavity may form under smaller or greater loads than the expected critical value. We refer to these phenomena as ‘likely cavitation’. Moreover, we provide examples of homogeneous isotropic incompressible materials exhibiting stable or unstable cavitation together with their stochastic equivalent.
各向异性应变能函数的随机场模型及其在血管力学不确定性量化中的应用
影响因子：
7.2
作者：
Staber, B.;Guilleminot, J.
通讯作者：
Guilleminot, J.