Abstract
Necking is an instability phenomenon widely observed in metallic and polymeric materials. On the basis of the minimum energy barrier criterion, we propose a theoretical method, combined with Monte Carlo simulations, to predict the linear instability and post-bifurcation behavior of materials with a non-convex constitutive law. For illustration, this method is applied to analyze the necking bifurcation behavior of a plate under uniaxial tension. Especially, we consider the effect of surface tension, which is important for the necking of polymeric materials. For soft materials with high surface energy, surface effects may greatly influence the morphological evolution of necking, such as the position and wavenumber of the consecutive necking zones. This work not only helps understand various necking phenomena in biological and engineering materials, but also can be extended to analyze some other instability problems, e.g., surface wrinkling.
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