Elastic Interaction of Pressurized Cavities in Hyperelastic Media: Attraction and Repulsion

Abstract This study computationally investigates the elastic interaction of two pressurized cylindrical cavities in a 2D hyperelastic medium. Unlike linear elasticity, where interactions are exclusively attractive, nonlinear material models (neo-Hookean, Mooney–Rivlin, Arruda–Boyce) exhibit both attraction and repulsion between the cavities. A critical pressure-shear modulus ratio governs the transition, offering a pathway to manipulate cavity configurations through material and loading parameters. At low ratios, the interactions are always attractive, while at high ratios, both attractive and repulsive regimes exist depending on the separation between the cavities. The effect of the strain-stiffening on these interactions is also analyzed. These insights bridge theoretical and applied mechanics, with implications for soft material design and subsurface engineering.