Abstract

Experimental evidence suggests that suction may play a role in the attachment strength of mushroom-tipped adhesive structures, but the system parameters which control this effect are not well established. A fracture mechanics-based model is introduced to determine the critical stress for defect propagation at the interface in the presence of trapped air. These results are compared with an experimental investigation of millimeter-scale elastomeric structures. These structures are found to exhibit a greater increase in strength due to suction than is typical in the literature, as they have a large tip diameter relative to the stalk. The model additionally provides insight into differences in expected behavior across the design space of mushroom-shaped structures. For example, the model reveals that the suction contribution is length-scale dependent. It is enhanced for larger structures due to increased volume change, and thus the attainment of lower pressures, inside of the defect. This scaling effect is shown to be less pronounced if the tip is made wider relative to the stalk. An asymptotic result is also provided in the limit that the defect is far outside of the stalk, showing that the critical stress is lower by a factor of 1/2 than the result often used in the literature to estimate the effect of suction. This discrepancy arises as the latter considers only the balance of remote stress and pressure inside the defect and neglects the influence of compressive tractions outside of the defect.

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