Adhesion and friction effects in soft contact mechanics: from shell buckling to viscoelastic rolling

This thesis presents a comprehensive study of the coupled effects of adhesion and friction in soft and thin-walled structures, with emphasis on how interfacial phenomena control deformation, stability, and energy dissipation. By combining theoretical analysis, numerical modeling, and classical experimental inspiration, the work aims to provide a unified understanding of adhesive contact mechanics in viscoelastic and compliant systems. The thesis begins with a detailed theoretical framework that reviews the fundamental mechanics of adhesive and frictional contact. Classical models such as those of Hertz, Johnson–Kendall–Roberts (JKR), Derjaguin–Muller–Toporov (DMT), and Maugis are discussed together with their extensions to viscoelastic and rough interfaces. The chapter also highlights the physical role of interface traction, surface energy, and time-dependent viscoelastic behavior, establishing the basis for the subsequent computational studies. The second part investigates the interplay of adhesion and friction in the mechanical stability of thin spherical shells in contact with rigid substrates. Through finite element simulations, it is shown that interfacial adhesion and friction can suppress the classical buckling instability by redistributing in-plane stresses and providing additional constraint against normal displacement. The results quantify how adhesion enhances the critical load for buckling and how friction introduces tangential stiffness, altering both the buckling mode and the post-buckling path. This study clarifies the dual stabilizing mechanisms of adhesive and frictional interactions and provides scaling relations linking adhesion energy, shell thickness, and curvature. The following chapter focuses on the sliding of a rigid cylinder on a viscoelastic adhesive substrate. Using a boundary element method (BEM) coupled with a cohesive-zone description based on the Lennard–Jones potential and the Standard Linear Solid model, the analysis explores the effect of the Maugis–Tabor parameter (λ) on the contact asymmetry and frictional dissipation. The results reveal that adhesion modifies the distribution of contact pressure and causes a velocity-dependent transition between adhesive and viscoelastic friction regimes, in agreement with theoretical predictions and experimental observations from polymer systems. The final part of the thesis is inspired by the classical experiments of Barquins and Roberts on the rolling of rigid cylinders over viscoelastic substrates. A numerical framework is developed to reproduce these experiments, combining adhesive traction and visicoelastic dissipation in a cohesive contact formulation. The simulations accurately reproduce the non-monotonic dependence of rolling resistance on velocity observed experimentally. Comparison with the Persson–Brener analytical theory (2010) confirms the validity of the model and elucidates the relative roles of adhesive hysteresis and bulk viscoelastic losses in determining the overall friction. This study bridges experimental findings and theoretical formulations, offering new insight into energy dissipation mechanisms in adhesive rolling contacts. Collectively, these studies establish a coherent multiscale framework for understanding adhesion–friction coupling in soft matter. By linking continuum mechanics, surface physics, and viscoelastic dissipation, the thesis advances predictive modeling of adhesive contacts across different loading modes—buckling, sliding, and rolling. The findings contribute to the broader understanding of soft tribology and have potential applications in flexible electronics, bio-inspired adhesion, and soft robotic interfaces, where control of adhesion and friction at compliant interfaces is essential.