Nanoadhesion of a power-law graded elastic material

The Dugdale-Barenblatt model is used to analyze the adhesion of graded elastic materials at the nanoscale with Young's modulus E varying with depth z according to a power law E = E0(z/C0)k (0 < k < 1) while Poisson's ratio v remains a constant, where E0 is a referenced Young's modulus, k is the gradient exponent and C0 is a characteristic length describing the variation rate of Young's modulus. We show that, when the size of a rigid punch becomes smaller than a critical length, the adhesive interface between the punch and the graded material detaches due to rupture with uniform stresses, rather than by crack propagation with stress concentration. The critical length can be reduced to the one for isotropic elastic materials only if the gradient exponent k vanishes.