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Initial Post-contact Behavior of an Axially Compressed Fiber Constrained Inside a Rigid Cylinder: Experimental, Analytical and Numerical Investigation


 The post-buckling behavior of a clamped-clamped elastic fiber constrained inside a rigid cylinder is analyzed theoretically, numerically, and experimentally. We concentrate on characterizing the contact configuration between the fiber and the cylinder wall during initial post-contact stages of the fiber deformation, in which only a small segment of the fiber length maintains contact with the cylinder wall. This is apparently the first study of that phenomenon presenting an in-depth investigation of the fiber deformation and contact stages in experiments, along with a detailed examination of the effect of fiber geometrical imperfection. The main experimental challenge was to identify regions of contact between the fiber and the cylinder wall, and to distinguish them from segments of the fiber that are very close to the cylinder wall but make no contact with it. To this end, we employed a novel experimental setup consisting of a transparent rigid cylinder filled with an opaque milky fluid, combined with image processing, and synchronized force measurements. The results of the experiments are supported by finite-element analysis and are also compared to available theoretical predictions based on the elastica model of an initially perfectly straight fiber. A small strain analytical solution reveals the role of minor initial geometrical imperfections in deriving the force-displacement relation during fiber bending. The study provides new understanding of the influence of key parameters on the behavior of such systems and may have practical implications in the fields of stent procedures, medical endoscopy, deep drilling, and more.