Push and Pull: Elastic Interaction Between Pressurized Spherical Cavities in Nonlinear Elastic Media

TL;DR

This study computationally investigates how pressurized spherical cavities in nonlinear elastic media interact, revealing complex behaviors such as attraction and repulsion depending on pressure and material properties, with implications for material design.

Contribution

It provides a detailed finite element analysis of cavity interactions in hyperelastic materials, highlighting the influence of pressure and strain-stiffening on interaction regimes and phase diagrams.

Findings

Negative pressures always attract cavities.

Positive pressures can cause non-monotonic energy landscapes.

Interaction behavior depends on material strain-stiffening parameters.

Abstract

Elastic interaction of pressurized spherical cavities embedded in a three-dimensional hyperelastic medium is computationally analyzed. Using finite element analysis across several positive and negative pressure scenarios, we calculate the system's potential energy and configurational driving force for neo-Hookean, Mooney-Rivlin, and Arruda-Boyce material models. Our results show that while the interaction is always attractive for negative pressures, a non-monotonic energy landscape emerges for positive pressures above a critical value. In this regime, cavities attract at close range and repel when further apart. The critical separation distance for this transition is shown to be dependent on the material's strain-stiffening parameters. These findings are consolidated into phase diagrams, providing a clear map of interaction behaviors.