Friction-induced contact and stability transitions in the post-buckling of beams confined by compliant walls

Abstract The post-buckling behavior of slender structures confined by deformable boundaries governs load transmission, steering capability, and jamming in systems such as guidewires, catheters, drill strings, and biological filaments. While wall compliance and friction have each been studied separately, their coupled influence remains largely unexplored. Here we show that introducing friction together with compliant confinement leads to a fundamentally different class of solutions, characterized by symmetry breaking, spatial force gradients, and new transition mechanisms not present in frictionless systems. To this end, we analyze a clamped-clamped slender beam confined between a rigid surface and a nonlinear spring-supported wall in the presence of Coulomb friction, thereby coupling frictional contact with compliant confinement. A reduced analytical model, supported by extensive numerical analysis, captures point-contact and line-contact configurations, rolling and slip regimes, transitions between contact states, and instability-induced switching to higher modes. We further demonstrate that friction can delay or suppress the onset of line contact and mode switching, induce non-monotonic force-displacement responses, and generate counterintuitive transitions from line contact back to point contact, as well as reversals from slip to rolling. Despite the complexity of the response, we show that the behavior is governed by two nondimensional parameters: the relative stiffness of the beam-wall system and a corrected friction coefficient accounting for friction and initial gap. Transition maps are constructed for the onset of line contact and mode switching, providing direct predictive criteria for confined slender systems with linear, stiffening, or softening wall response.