Specific adhesion of soft elastic half spaces via molecular bond clusters has been extensively studied in the past ten years. In this study, the adhesion of a soft elastic solid with finite size is considered aiming to investigate how their size and shape may affect the adhesion strength. To model this problem, plane strain assumption is adopted to describe the deformation of the elastic solid. This deformation couples the stochastic behavior of adhesive bonds, for which we have considered the mean field treatment based on the classical Bell theory. Numerical solutions have revealed that, besides the elastic modulus, size of the elastic solid and spatial arrangement of the bond clusters are all crucial factors in mediating the adhesion strength. Most interestingly, there clearly exists an optimal size/shape of the elastic solid that corresponds to the largest adhesion strength. These findings provide new insights and inspirations in understanding various phenomena of cellular adhesion and designing advanced functional biomaterials.

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