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Abstract: In the present paper, the mechanics of axisymmetric adhesive contact of rough surfaces involving power-law graded materials is investigated analytically. A series of general analytical solutions have been obtained with use of the cumulative superposition and equivalent energy release rate approaches. These solutions provide closed-form expressions of equilibrium relations among applied load, indentation depth and contact radius. Based on these solutions, an effective macroscopic description of the contact evolution is obtained for a general punch profile with surface roughness. Our analysis results reveal that the simultaneous presence of surface roughness and graded material properties can influence the pull-off force and energy dissipation due to adhesion hysteresis significantly. Moreover, it is found that both the adhesion strength and toughness can be optimized by adjusting the surface topography and material parameters of power-law graded solids appropriately. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials as special cases and therefore can also serve as the benchmarks for checking the validity of numerical solution results. [Copyright &y& Elsevier]

Abstract: In previous work about axisymmetric adhesive contact on power-law graded elastic materials, the contact interface was often assumed to be frictionless, which is, however, not always the case in practical applications. In order to elucidate the effect of friction and the coupling between normal and tangential deformations, in the present paper, the problem of a rigid punch with a parabolic shape in non-slipping adhesive contact with a power-law graded half-space is studied analytically via singular integral equation method. A series of closed-form analytical solutions, which include the frictionless and homogeneous solutions as special cases, are obtained. Our results show that, compared with the frictionless case, the interfacial friction tends to reduce the contact area and the indentation depth during adhesion. The magnitude of the coupling effect depends on both the Poisson ratio and the gradient exponent of the half-space. This effect vanishes for homogeneous incompressible as well as for linearly graded materials but becomes significant for auxetic materials with negative Poisson’s ratio. Furthermore, influence of mode mixity on the adhesive behavior of power-law graded materials, which was seldom touched in literature, is discussed in details. [Copyright &y& Elsevier]

Highlights • Constructs the Hertzian piezoelectric contact model by cumulative superposition for a rigid punch of general profile. • Establishes the JKR-type adhesive contact model for a rigid conducting punch of power-law profile with use of the developed equivalent energy release rate approach. • Develops a series of closed-form analytical solutions which include the classical Hertz- n and JKR- n solutions as special cases. • Reveals the effect of shape index on indentation responses of piezoelectric materials in the non-adhesion and JKR adhesion regimes. Abstract The present paper provides a theoretical study on the axisymmetric contact and adhesive behaviors of a transversely isotropic piezoelectric half-space under a rigid punch, with an emphasis on Hertzian contact and JKR-type adhesion solutions for the conducting punch of power-law profile. The Hertzian piezoelectric contact model and JKR-type adhesion model are established by cumulative superposition and equivalent energy release rate approaches, respectively. Closed-form expressions are derived for the applied load, indentation depth, distributions of contact traction and surface displacement, which are able to link existing solutions for non-adhesive and adhesive contact problems for transversely isotropic and isotropic elastic materials, and to include the corresponding Hertz- n and JKR- n solutions as special cases. Similar mathematical forms are found between the elastic solids and the piezoelectric materials under a conducting grounded punch except for different material moduli. These results can serve as benchmarks for checking the validity of numerical methods. [ABSTRACT FROM AUTHOR]