On shear adhesion of adhesive fibrils

Natural fibrillar adhesives, widely recognized for their strong and reversible adhesion, have inspired the development of numerous synthetic adhesive systems applied in diverse fields. These biological and bioinspired adhesive fibrils exhibit a wide range of aspect ratios spanning four orders of magnitude. Accurate prediction of their adhesion performance is crucial for their practical applications. Prior investigations have primarily focused on adhesion under normal loading, although shear loading is also commonly encountered in various scenarios. To date, only a few shear adhesion models exist, and they are limited to either high or low aspect ratios. Rigorous mechanics analysis of adhesive fibrils’ shear adhesion strength across a wide range of aspect ratios is lacking. In this study, we developed a mechanics model based on the compliance method for evaluating the energy-controlled interfacial failure of the adhesive fibrils, estimated the shear adhesion strength of a lap shear system across a wide range of fibrillar aspect ratios, and carried out the finite element analysis (FEA) to validate the model prediction. Our model reveals that, depending on the fibrillar aspect ratio, the adhesive fibril exhibits three distinct deformation regimes: thin film shearing, thick block shearing, and slender beam bending. The important parameters governing the shear adhesion of the lap shear system are the aspect ratio of fibrils, elastic moduli of the fibrils and substrates, while the Poisson's ratio of fibrils has no noticeable effect. Our model captures the shear compliance across a wide aspect ratio range from 10⁻⁴ to 10² accurately and is in excellent agreement with the FEA results. Based on this compliance solution, a rigorous scaling law for shear adhesion strength is derived, which can predict the energy-controlled adhesion regime as well as the theoretical strength-limited regime, as the aspect ratio decreases. These results reveal the underlying mechanisms governing the shear adhesion strength of fibrillar adhesives and provide guidance for future design and optimization of fibrillar adhesives. © 2023 Elsevier Ltd.