The effect of interactions on elastic cavitation

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. In realistic settings the cavitation threshold is influenced by proximity to interfaces and interactions with neighboring 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 (≈ 3.5μ) 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 half-distance d: the threshold approaches the bulk value for distant cavities and reaches a maximum of ≈ 2.67μ at d ≈ 3.78R, where R is the initial cavity radius. These results provide, for the first time, a quantitative estimate of cavitation pressure for these two interaction-effect extensions of the classical cavitation problem and will help guide modeling of cavitation-driven processes in porous, biological, and multi-material solids.