Adhesives based on fibrillar surface microstructures have shown great potential for handling applications requiring strong, reversible, and switchable adhesion. Recently, the importance of the statistical distribution of adhesive strength of individual fibrils in controlling the overall performance was revealed. Strength variations physically correspond to different interfacial defect sizes, which, among other factors, are related to surface roughness. For analysis of the strength distribution,

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... Weibull's statistical theory of fracture was introduced. In this study, the importance of the statistical properties in controlling the stability of attachment is explored. Considering the compliance of the loading system, we develop a stability criterion based on the Weibull statistical parameters. It is shown that when the distribution in fibril adhesive strength is narrow, the global strength is higher but unstable detachment is more likely. Experimental variation of the loading system compliance for a specimen of differing statistical properties shows a transition to unstable detachment at low system stiffness, in good agreement with the theoretical stability map. This map serves to inform the design of gripper compliance, when coupled with statistical analysis of strength on the target surface of interest. Such a treatment could prevent catastrophic failure by spontaneous detachment of an object from an adhesive gripper.