[论文解读] The effect of interactions on elastic cavitation

Ali Saeedi, S Chockalingam+1 more|arXiv (Cornell University)|Mar 20, 2026

Ultrasound and Cavitation Phenomena被引用 0

一句话总结

论文量化了刚性界面近邻和另一个腔体近邻如何改变不可压缩 neo-Hookean 实体在远场静水张力下的空化阈值，在界面附近 p_c 约为 3.44μ，且两腔近邻时呈现非单调的 p_c 峰值约为 2.67μ。

ABSTRACT

Cavitation refers to the sudden, unstable expansion of a defect or cavity within a material in response to applied loads, when the loads reach a critical threshold. It is widely recognized as a common failure nucleation mechanism in soft and biological materials. For an isolated cavity in the bulk of an incompressible neo-Hookean solid loaded by remote hydrostatic tension, the classical cavitation pressure is well established as $2.5 μ$, where $μ$ is the shear modulus. However, in realistic settings the cavitation threshold is influenced by interaction of the cavity with nearby interfaces and other cavities. Interface interaction effects are particularly relevant in multi-material systems and additively manufactured structures, where defects frequently occur near material boundaries. Meanwhile, cavity-cavity interactions become important in materials exhibiting finite porosity, such as foams, porous solids, and phase-separating polymers. Here, we characterize the effect of interactions on cavitation pressure for (i) a nearby rigid interface and (ii) a neighboring identical cavity. For cavities near a rigid interface, our analysis shows that the cavitation pressure increases as the initial cavity-interface distance decreases, starting from the bulk value for a distant cavity and approaching the cavitation pressure value for a defect situated at an interface ($\approx3.5μ$) as the cavity approaches the interface boundary. In contrast, interacting cavities exhibit a non-monotonic dependence of the cavitation pressure on the initial inter-cavity distance $d$: the threshold approaches the bulk value of $2.5μ$ for distant cavities and reaches a maximum of $\sim2.8μ$ at $d\sim5.7R$, where $R$ is the initial cavity radius.

研究动机与目标

• 理解空化作为软物质与生物材料中单个缺陷之外的失效机制的动机。
• 量化近旁刚性边界和相邻腔体如何改变空化阈值。
• 为考虑相互作用的配置提供实用的空化压力估算，以指导多孔/多材料系统的建模。

提出的方法

• 将介质建模为不可压缩的 neo-Hookean 体，W=(μ/2)(I1−3)。
• 分析两种轴对称配置在远场静水张力下的行为：一个腔体靠近刚性界面，以及两个相同且彼此接近的腔体。
• 采用位移控制加载，通过将腔体体积变化与外部边界位移的施加联系起来来跟踪空化。
• 使用 FEniCS 解算，采用混合位移–压力形式与扰动拉格朗日约束（J−1=ṗ/K）。
• 通过在 V̄^(−1/3) 的 Laguerre 多项式基上对模拟的 p–V 数据进行曲线拟合，并外推到 V̄→∞ 来提取空化压力。

Figure 1 : Axisymmetric schematic of the cavitation problems being studied: (a) cavity-interface interaction, and (b) cavity-cavity interaction. The cavities are under remote hydrostatic tension loading.

实验结果

研究问题

• RQ1 刚性界面邻近如何影响不可压缩 neo-Hookean 实体中球形腔体的空化压力？
• RQ2 相邻的相同腔体存在如何使空化压力随腔体间距的变化而变化？
• RQ3 界面与腔体相互作用情形下的空化压力相对体积值的定量极限是多少？
• RQ4 是否存在鲁棒的外推方法可以从有限体积的模拟中可靠估计渐近的空化压力？

主要发现

• 对于靠近刚性界面的腔体，随着腔体靠近界面，p̄_c 增大，在 d/R=1.1 处达到 p̄_c≈3.44，且当 d/R→∞ 时趋近于体相值 p̄_c,bulk=2.5。
• 在无限介质中的两个相同腔体，p̄_c 以非单调方式随腔体间距半径比 d/R 变化，在 d/R≈3.8 时达到峰值 p̄_c≈2.67，且当分离增大时趋近体相值 2.5。
• 界面空化压力为 p̄_c,int≈3.5，该值用于描述在刚性界面缺陷处的空化压力，表明边界约束显著提高空化压力。
• 研究证实界面与腔体相互作用均会对空化压力产生可观的提升，为多孔、生物和多材料固体中的空化驱动过程建模提供了定量基准。

Figure 4 : Deformed cavity shapes in (top) cavity-interface interaction and (bottom) cavity-cavity interaction problems for different dimensionless volumes.