Characterization of the Functionally Graded Shear Modulus of a Half-Space

Abstract

In this article, a method is proposed for determining parameters of the exponentialy varying shear modulus of a functionally graded half-space. The method is based on the analytical solution of the problem of pure shear of an elastic functionally graded half-space by a strip punch. The half-space has the depth-wise exponential variation of its shear modulus, whose parameters are to be determined. The problem is reduced to an integral equation that is then solved by asymptotic methods. The analytical relations for contact stress under the punch, displacement of the free surface outside the contact area and other characteristics of the problem are studied with respect to the shear modulus parameters. The parameters of the functionally graded half-space shear modulus are determined (a) from the coincidence of theoretical and experimental values of contact stresses under the punch and from the coincidence of forces acting on the punch, or (b) from the coincidence of theoretical and experimental values of displacement of the free surface of the half-space outside the contact and coincidence of forces acting on the punch, or (c) from other conditions. The transcendental equations for determination of the shear modulus parameters in cases (a) and (b) are given. By adjusting the parameters of the shear modulus variation, the regions of “approximate-homogeneous” state in the functionally graded half-space are developed.

A Receding Contact Problem of Two Layers one of Functionally Graded, Loaded by Circular Rigid Block and Resting on a Pasternak Foundation

“…The quasi-static frictional contact problem of a rigid rounded punch sliding over a bidirectionally graded half-plane within the framework of plane strain elasticity was examined by Arslan [20]. A method for determining the parameters of the exponentially varying shear modulus of an FG half-space was proposed by Zelentsov et al [21]. The effect of punch speed on frictional contact mechanics of finite-thickness graded layer resting on the rigid foundation researched by Balcı [22].…”

Soft Contact Mechanics with Gradient-Stiffness Surfaces

“…A variety of analytical elasticity solutions exist, − and may be helpful, but they have limited applicability to solve for local gradient properties of complex biological and soft samples because of the advanced approaches and solution methods required. Zelentsov et al attempted to bridge this by providing simplified solutions, but they still require simplification of a gradient surface into pseudo-homogeneous regions. The authors believe that the complexity of the theoretical approaches or the reliance on elasticity in the small-strain limit has prevented adoption to the indentation data taken on biological and soft materials.…”

Functionally Graded Piezoelectric Medium Exposed to a Movable Heat Flow Based on a Heat Equation with a Memory-Dependent Derivative

“…These novel nonhomogeneous materials have excellent thermo-mechanical properties and have broad applications to vital structures, for example, atomic reactors, pressure vessels, chemicals plants, aviation, and channels, and so on. The problems of a functionally graded elastic half-space are considered by many researchers [4][5][6][7][8][9].…”