Numerical simulation of the edge stress singularity and the adhesion strength for compliant mushroom fibrils adhered to rigid substrates

Bio-inspired adhesion of micropatterned surfaces due to intermolecular interactions has attracted much research interest over the last decade. Experiments show that the best adhesion is achieved with compliant "mushroom"-shaped fibrils. This paper analyses numerically the effects of different mushroom shapes on adhesion to a rigid substrate. When a remote stress is applied on the free end of a fibril perfectly bonded to a rigid substrate, the resultant stress distribution along the fibril is found to change dramatically between the straight punch and mushroom fibrils. A singular stress field is present at the edge of the fibril where it contacts the substrate and, in this work, the amplitude of the singularity is evaluated for fibrils perfectly bonded to a flat substrate so that sliding cannot occur there. This exercise is carried out for fibril geometries involving combinations of different diameters and thicknesses of the mushroom cap. By assuming a pre-existing detachment length at the corner where the stress singularity lies, we predict the adhesive strength for various mushroom cap shapes. Our study shows that a smaller stalk diameter and a thinner mushroom cap lead to higher adhesive strengths. A limited number of results are also given for other shapes, including those having a fillet radius connecting the stalk to the cap. The results support the rational optimisation of synthetic micropatterned adhesives.