Carbone and Pierro (Meccanica 48, 1819--1833 (2013)) discuss that punch shaped ends give less strong adhesion than mushrooms-ended ones because of the stress singularity at the corner. In particular, they assume large friction at the interface, which leads close to the classical Linear Elastic Fracture Mechanics singularity, corresponding to the classical scaling with the flat punch shaped pillar radius for what they call mode I of failure, ruled by the so-called Kendall formula. Their calculations are valid assuming perfect bonding for both punch or mushroom shaped ends.
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