Optimal grading of elastic modulus at contact corners with friction with application in fibrillar adhesives

Recent studies have reported that micropillars composed of graded materials exhibit high adhesion performance in fibrillar adhesive systems. To uncover the origin of this enhanced performance and further promote the application of graded materials, we investigate the general contact mechanics of wedges composed of power-law graded materials. Our findings show that the stress singularity at the apex of the wedge can be eliminated by increasing the exponent of the power-law modulus. For cases with perfectly bonded interfaces, frictionless interfaces, and interfaces with Coulomb friction, the critical conditions for eliminating stress singularities are presented, thereby suggesting how to obtain optimal designs.