Compressibility-regulated elasto-capillary necking and bulging in soft solids

In recent years, there has been a burgeoning interest in elasto-capillary instability in soft solids. Given that most soft matter is compressible, elucidating the effect of bulk compressibility on the post-bifurcation behaviors of Plateau–Rayleigh (PR) instability in solid-like materials is essential, yet this issue remains unresolved. In this paper, we investigate elasto-capillary necking/bulging instabilities in a compressible soft hyperelastic cylinder subjected to axial force and strain-dependent surface stresses. A one-dimensional (1D) reduced model is employed to derive the fully nonlinear post-bifurcation solutions. The validity of the 1D asymptotic results is confirmed by three-dimensional (3D) finite element (FE) simulations. Based on the bifurcation and post-bifurcation results across different loading scenarios, we systematically analyze and elucidate the role of bulk compressibility in the complex bulk–surface interactions. The thorough systematic analyses reveal that bulk compressibility not only plays a pivotal role in mediating bulk–surface deformation but also dictates the sensitivity of instability behaviors to surface parameters, axial force, and geometrical size. Specific guidelines to modulate elasto-capillary necking/bulging in solid-like materials through the rational utilization of bulk compressibility are provided. These findings are beneficial for the design and application of soft solid materials and structures.