Bubble dynamics in a viscoelastic medium with nonlinear elasticity
Bubble dynamics in a viscoelastic medium with nonlinear elasticity
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DOI：
10.1017/jfm.2015.7
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发表时间：
2015-03-01
影响因子：
3.7
通讯作者：
Johnsen, E.
中科院分区：
文献类型：
--
作者：
Gaudron, R.;Warnez, M. T.;Johnsen, E.
在最近开发的各种医疗程序中，气泡直接在软组织中形成，并可能导致损伤。虽然牛顿液体中的空化现象受到了极大的关注，但粘弹性介质组织中的气泡动力学仍然知之甚少。为了模拟组织，大多数以前的研究都集中在麦克斯韦粘弹性流体。然而，软组织通常具有变形后松弛的原始构型。因此，基于Kelvin-Voigt的粘弹性模型预计是更合适的表示。此外，可能会发生大的振荡，从而违反了无穷小应变假设，需要一个非线性/有限应变弹性描述。在这篇文章中，我们开发了一个理论框架来模拟球形气泡动力学的粘弹性介质与非线性弹性。按照现代连续介质力学的形式主义，我们推导出的形式的弹性力作用在一个气泡上的常见的应变能函数（如新Hookean，Mooney-Rivlin），并将它们纳入Rayleigh-Plesset方程。非线性弹性的主要作用是降低了大偏离平衡半径时的坍塌和回弹的剧烈程度，并增加了振荡频率。本方法可以很容易地扩展到其他应变能函数，并用于计算周围介质中的应力/变形场。
In a variety of recently developed medical procedures, bubbles are formed directly in soft tissue and may cause damage. While cavitation in Newtonian liquids has received significant attention, bubble dynamics in tissue, a viscoelastic medium, remains poorly understood. To model tissue, most previous studies have focused on Maxwell-based viscoelastic fluids. However, soft tissue generally possesses an original configuration to which it relaxes after deformation. Thus, a Kelvin-Voigt-based viscoelastic model is expected to be a more appropriate representation. Furthermore, large oscillations may occur, thus violating the infinitesimal strain assumption and requiring a nonlinear/finite-strain elasticity description. In this article, we develop a theoretical framework to simulate spherical bubble dynamics in a viscoelastic medium with nonlinear elasticity. Following modern continuum mechanics formalism, we derive the form of the elastic forces acting on a bubble for common strain-energy functions (e.g. neo-Hookean, Mooney-Rivlin) and incorporate them into Rayleigh-Plesset-like equations. The main effects of nonlinear elasticity are to reduce the violence of the collapse and rebound for large departures from the equilibrium radius, and increase the oscillation frequency. The present approach can readily be extended to other strain-energy functions and used to compute the stress/deformation fields in the surrounding medium.