Scale Effect of Optimized Geometry of Mushroom-Shaped Biomimetic Adhesive Structures Adhered to Rigid Substrates

Mushroom-shaped microstructures (MMFs) inspired by gecko feet have attracted significant attention owing to their superior adhesion performance. Previous studies reveal that the adhesive behavior of these structures depends on their geometric dimensions, yet the coupled effects of different characteristic sizes and their corresponding optimized configurations remain insufficiently elucidated. This study investigates the contact adhesion between polydimethylsiloxane (PDMS)-based (MMFs) and rigid substrates through integrated experimental characterization techniques (including in situ observations) and high-fidelity numerical simulations. Experimental and numerical results showed that when maintaining constant dimensional proportions in MMFs, adhesion strength decreases with increasing cap size from the micrometer to millimeter scale, exhibiting a distinct three-regime characteristic, wherea sthe debonding mechanism transitions from center-crack to edge-crack mode. Notably, a stable adhesion strength plateau exists within the scale range of tens of micrometers to several millimeters, where pull-off force can be enhanced by increasing structural dimensions. The optimized geometric configuration of MMFs shows significant scale dependence: as cap size increases from several micrometers to hundreds of micrometers or millimeters, the optimal stalk-to-cap diameter ratio decreases from 0.9 to 0.85, while the optimal cap thickness evolves synergistically with the diameter ratio, with the optimal cap thickness-to-stalk diameter ratio ranging between 0.057 and 0.1.