Elasto-capillary necking, bulging and Maxwell states in soft compressible cylinders

Localized pattern formations and "two-phase" deformations are studied theoretically in soft compressible cylinders subject to surface tension axial loading through several force-controlled scenarios. By drawing upon known results for separate yet mathematically similar elastic localization problems, a concise family of analytical bifurcation conditions localized bulging or necking derived terms general strain energy function. The effect material compressibility strain-stiffening behaviour on the point is analysed, comparisons between our theoretical corresponding numerical simulation Dortdivanlioglu Javili (Extreme Mech. Lett. 55, 2022) made. It then explained how fully developed (Maxwell) state which evolves from initial solution can be comprehensively understood using simple expressions force parameters primary deformation. power this approach validating phase-separation-like problems nature highlighted