Surface effect on the necking of hyperelastic materials

Necking is a widely observed instability phenomenon. Surface tension often plays a significant role in the deformation of soft materials, especially at the micro scale, but its influence on the necking behavior of soft structures remains unclear. In this paper, we use the energy method to explore surface effects on the necking of soft plates and cylindrical bars under uniaxial tension. Analytical solutions are derived for the critical conditions of necking instability in the two types of structural components with a power-law constitutive relation. It is found that surface energy shows different impacts on their necking behaviors – it tends to postpone the occurrence of necking in soft plates but promote that in soft cylinders. This work not only deepens our understanding of the instability of soft materials but also helps design soft devices and robots.