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

Abstract

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.

Cellular buckling from mode interaction in I-beams under uniform bending

“…It has been found to be prevalent in systems where there is progressive destabilization and subsequent restabilization (Wadee & Bassom 2000;Peletier 2001), such as in cylindrical shell buckling (Hunt et al 1999(Hunt et al , 2003 and kink banding in confined layers (Hunt et al 2000b;Wadee & Edmunds 2005). In the fundamental studies concerning the model strut on a nonlinear foundation, the load oscillates about the Maxwell load, where the buckling modes progressively transform from localized (homoclinic) profiles to a periodic mode in a heteroclinic connection (Budd et al 2001;Wadee et al 2002;Chapman & Kozyreff 2009).…”

Sequential Buckling: A Variational Analysis

“…At a given time the resulting profile shows a periodic section flanked by decaying tails; as the shortening increases the periodic section widens. Similar examples of localization followed by spreading are found in axially loaded cylinders [14,8], in sandwich structures [9], and in kink banding in layered materials [10]. The survey paper [9] discusses these examples from a common perspective.…”

Effects of thickness and fibre misalignment on compression fracture in cross-ply (very) long cylindrical shells under external pressure

“…Chaudhuri & Kim [36] for a detailed discussion), for a very thick elastic (very) long cylindrical shell (R i /h = 3), and sufficiently higher average fibre misalignment (φ/γ f = 1.5). Maxwell's construction has also been employed by Hunt & Lucena Neto [59], Budiansky et al [60], Hunt et al [61] and Wadee & Edmunds [62] for similar purposes.…”