Large-Deflection Nonlinear Mechanics of Curved Cantilevers Under Contact Point Loading

Presented here is a comprehensive model for hook bending behavior under contact loading conditions, motivated by the relevance of this problem to reusable hook attachment systems in nature and engineering. In this work, a large-deflection model that can describe the bending of hooks, taken as precurved cantilevers with uniform initial curvature, was derived and compared with physical testing. Physical testing was performed with stainless-steel and aluminum hooks shaped as semicircular arcs. The force versus displacement behavior exhibited a linear portion for small displacements but at large displacements there was an asymptotic relation where the force approached some limit and remained flat as further displacement occurred. Comparison with testing showed that the model developed in this paper gave good agreement with the physical testing. Surprisingly, in dimensionless form, all parameters to define the hook transform to approximately linear functions of displacement. Using these linear relations, several equations are presented that allow for rapid calculation of the dimensional force versus displacement for a hook.