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

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.