Adhesive behavior of two-dimensional power-law graded materials

In this paper, we investigate the adhesive contact between a rigid cylinder of radius R and a graded elastic half-space with a Young's modulus varying with depth according to a power-law, E = E₀ (y / c₀)^k (0 < k < 1), while the Poisson's ratio ν remains constant. The results show that, for a given value of ratio R / c₀, a critical value of k exists at which the pull-off force attains a maximum; for a fixed value of k, the larger the ratio R / c₀, the larger the pull-off force is. For Gibson materials (i.e., k = 1 and ν = 0.5), closed-form analytical solutions can be obtained for the critical contact half-width at pull-off and pull-off force. We further discuss the perfect stick case with both externally normal and tangential loads.