Simplified kink banding: a predictive model for localized failure in layered structures

The phenomenon on kink banding, occurring primarily in layered structures under layer-parallel compression, has been studied extensively in a variety of different situations. Examples of physical systems which exhibit this phenomenon include the deformation of geological strata [1, 2], compressed laminated fibre composites [3, 4, 5], and internally in fibre and wire ropes [6]. In our earlier work, the focus was on the geological application of kink banding where layers are confined by pressure and therefore penalize the formation of voids in the structure. Some of the technical difficulties that are encountered in the modelling of such systems were outlined in terms of using continuum mechanics and Cosserat-type continua. The approach we adopted involved formulating a model that cut out most of the complexity, but kept large rotations—the nonlinearity that seems to govern the structural response. This simple model exhibits a path of pure squash and a path of deformation where the kink bands form and rotate. However, as the paths of equilibrium cross at infinity, i.e. there exists an infinite critical load, from the linearized viewpoint there is no such instability, a conclusion that is not confirmed by experimental evidence which clearly shows the structure deforming suddenly after a certain amount of loading. The Maxwell stability criterion [7] was used in an earlier paper to overcome this difficulty [8]. This allowed the evaluation of a robust lower bound of the displacement where the system jumped from the undeformed to the kinked state, and the evaluation of the lock-up angle of the kink band. In the current study, several enhancements of the original model are outlined such that quantitative comparisons can be made between experiments and theory away from the neighbourhood of the initial instability and significantly into the post-kinking regime. It is found that not only can the new model embrace mechanisms for band propagation, in terms of band broadening and progression, but that comparisons of the band width and orientation against experiments are excellent. 2 Model Characteristics