**Abstract: **Delamination of rigid objects from an elastic substrate with finite thickness is a fundamental problem underlying applications such as marine fouling release coatings or anti-icing coatings. Most existing theoretical studies assume that delamination is driven by forces normal to the substrate surface, while in practice the delamination force may also include shear components that are parallel to the substrate surface. In this work, we consider a model system where a rigid cylindrical punch is detached from an elastic substrate under normal force, shear force or both. Our focus is to determine the pull-off force and to reveal the delamination mechanics under various geometrical and loading conditions, specifically the substrate thickness and the position and angle of the delamination force. To gain theoretical insights, we first study a plane strain model where a long rigid strip is adhered to an elastic half-space, and obtain an analytical solution revealing how the pull-off force depends on the loading position and angle. Moreover, we develop a three-dimensional finite element model to simulate the delamination of a rigid cylindrical punch from an elastic substrate with finite thickness. Three delamination modes are identified from finite element results: Mode-I crack propagation, Mode-II crack propagation, and interface cavitation. For the first two modes, we obtain empirical formulas to calculate the pull-off force using adhesion energy, substrate modulus, contact radius and substrate thickness. We also find that the analytical solution derived from the plan strain model can serve as a qualitative guide to estimate the effect of loading position and angle on the pull-off force.

**Sun, X., Yu, L., Rentschler, M.E., Wu, H., Long, R., "Delamination of a Rigid Punch from an Elastic Substrate Under Normal and Shear Forces," Journal of the Mechanics and Physics of Solids. 122: 141-160, 2019.**