The Maxwell stability criterion in pseudo-energy models of kink banding

Kink banding, common to many structures in nature and engineering, has several distinctive features---notably highly nonlinear snap-back instability leading to localization and sequential lock-up. The proposed friction model, although simplified, introduces these defining characteristics without obscuring them by including other effects of lesser immediate significance. In the absence of small imperfections or disturbances, linearized theory suggests that in its pre-kinked configuration the system never goes unstable. However, under sufficient applied end-displacement it is shown to be in a state of extreme metastability, such that micro-disturbances would trigger the nonlinear response. To overcome this problem we adopt an energy approach based on a global rather than a local stability criterion. When applied to imperfect systems with small initial misalignments, the critical displacement thus defined shows little of the sensitivity expected from other stability criteria, and provides a useful lower bound on the expected critical displacement and associated load. We offer the frictional model not as a complete description, but as a prototype to which other components can be added. Thus it provides information on the triggering, localization and lock-up processes, for example, but not on the choice of kink band width which is fixed a priori. Suggestions are provided throughout of extra energy contributions which will extend the model's capability.