Gecko-inspired fibrillar adhesives have attracted much attention and have good application prospects in many fields. Rate-dependent adhesion of the fibrillar adhesives is a commonly observed but less discussed issue, particularly for mushroom-shaped structures. Mushroom-shaped structures have become a popular design in recent ten years due to the optimal interfacial stress and thus better adhesion performance than the traditional flat-ended structure. However, the rate-dependent adhesion in mushroom-shaped structures is far less known. In this study, we do a preliminary study with a focus on the influence of retraction velocity on the pull-off force of the mushroom-shaped adhesive structure. Two mechanical models corresponding to two typical crack propagation modes (center crack and edge crack), respectively, are established to describe the pull-off dynamics. It is found that the pull-off force-velocity relation shows a power law at large velocities for both two crack propagation modes. The power exponent is about 0.2, almost the same for both modes, when the power exponent in the Gent-Schultz law is equal to 0.5. This power exponent value is found to be consistent with experiments. This study would provide theoretical insight into the rate-dependent adhesion of mushroom-shaped adhesive structures and promote optimal designs in related applications.

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