Adhesion model of side contact for an extensible elastic fiber

• A new adhesion model is proposed to predict the directional adhesion law of a straight extensible fiber.
• The applicable conditions of the Rivlin model, Kendall model and the inextensible side contact model in such an adhesion problem are quantified.
• Influences of the bending and axial stiffness on the maximum normal pull-off force are discussed.
• Generating an optimal pre-tension can maximize the maximum normal pull-off force.

For accurately predicted adhesion laws of fibrillar structures contribute to the rational design of high-performance biomimetic adhesives, an adhesion model is proposed to study the directional adhesion behavior of an extensible elastic fiber that contacts a rigid smooth surface with its side surface under the coupling effect of normal and shear forces, based on the extensible Euler Bernoulli beam theory and the surface energy concept. The deformed configuration of the fiber is obtained analytically, and on the basis of this result, the detachment mode and the normal pull-off force of the fiber for a given shear force are predicted directly. It is also found that, due to the extensibility of the fiber, there exists a maximum normal pull-off force (MNPF) when an optimal shear force is applied. The MNPF will be enhanced by increasing the axial stiffness, and reduced by increasing the bending stiffness. In addition, generating an optimal pre-tension in the adhered part of the fiber will maximize the MNPF. The derived adhesion law is expected to contribute to the optimal design and applications of single-level fibrillar adhesives.