The effect of interactions on elastic cavitation

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.

Figures (9)

• 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.
• Figure 2: Cavitation near a rigid interface: (a) dimensionless pressure--volume curves for different dimensionless cavity--interface distances $d/R=\{1.1, 3, 6, 20\}$. The dashed black curve shows analytical bulk cavitation case (eq. \ref{['eq:Pc_analytical']}); (b) dimensionless cavitation pressure as a function of $d/R$.
• Figure 3: Cavitation of two interacting cavities: (a) dimensionless pressure-volume curves of two interacting cavities for different dimensionless inter-cavity half-distances $d/R=\{1.1, 3, 6, 20\}$. The dashed black curve shows analytical bulk cavitation case (eq. \ref{['eq:Pc_analytical']}); (b) dimensionless cavitation pressure as a function of $d/R$.
• Figure 4: Deformed cavity shapes in (top) cavity-interface interaction and (bottom) cavity-cavity interaction problems for different dimensionless volumes.
• Figure 5: Axisymmetric schematic of the cavitation problem and its simulation model for the case of (a) cavity-interface interaction, and (b) cavity-cavity interaction. Both load-controlled and displacement-controlled representations are shown.