Receding contact problem for two-layer functionally graded media indented by a rigid punch

Çömez, İsa; El-Borgi, Sami; Kahya, Volkan; Erdol, Ragip

doi:10.1007/s00707-016-1648-8

Cited by 35 publications

(12 citation statements)

References 34 publications

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“…In particular, the results obtained from the semianalytical method are validated against those of the finite-element model. Given the physical nature of receding contact, the problem is more ideally modeled as a two-dimensional plane strain problem [11, 13, 16, 21]. In both methods, the Poisson ratio is set to ν = 0 . 25 ( κ = 2 ).…”

Section: Resultsmentioning

confidence: 99%

“…Rhimi et al [17] revisited the problem by replacing the half-plane substrate with a three-dimensional semi-infinite one. On the basis of fundamental FGM-substrate geometry, further extensions have also been developed, including the employment of an indenter [18], a homogeneous elastic substrate of finite thickness [19], a substrate consisting of two quarterplanes [20], and an FGM substrate of finite thickness [21]. By replacing the single FGM layer with an FGM–layer composite, perfectly bonded along their interface, we recently examined the effect of FGM inhomogeneity level on plane receding contact parameters [22, 23].…”

Section: Introductionmentioning

confidence: 99%

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A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

Yan

Liu

2017

Mathematics and Mechanics of Solids

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In this work, we examine the receding contact between a homogeneous elastic layer and a half-plane substrate reinforced by a functionally graded coating. The material properties of the coating are allowed to vary exponentially along its thickness. A distributed traction load applied over a finite segment of the layer surface presses the layer and the coated substrate against each other. It is further assumed that the receding contact between the layer and the coated substrate is frictionless. In the absence of body forces, Fourier integral transforms are used to convert the governing equations and boundary conditions of the plane receding contact problem into a singular integral equation with the contact pressure and contact size as unknowns. Gauss–Chebyshev quadrature is subsequently employed to discretize both the singular integral equation and the force equilibrium condition at the contact interface. An iterative algorithm based on the method of steepest descent has been proposed to numerically solve the system of algebraic equations, which is linear for the contact pressure but nonlinear for the contact size. Extensive case studies are performed with respect to the coating inhomogeneity parameter, geometric parameters, material properties, and the extent of the indentation load. As a result of the indentation, the elastic layer remains in contact with the coated substrate over only a finite interval. Exterior to this region, the layer and the coated substrate lose contact. Nonetheless, the receding contact size is always larger than that of the indentation traction. To validate the theoretical solution, we have also developed a finite-element model to solve the same receding contact problem. Numerical results of finite-element modeling and theoretical development are compared in detail for a number of parametric studies and are found to agree very well with each other.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

Yan

Liu

2017

Mathematics and Mechanics of Solids

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“…The receding contact problems of multi-layered elastic structures involving FGM also attracted extensive attention. The frictionless/frictional receding contact of bi-FGlayers were studied successively [31,32]. Then, the receding contact difficulties between an FGM-coated layer and a homogeneous half-plane pressed by a rigid cylindrical indenter were analyzed [33,34].…”

Section: Introductionmentioning

confidence: 99%

Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

Yan

2022

Crystals

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This paper studies a receding contact problem of a functionally graded layer laminate pressed against a functionally graded coated homogeneous half-plane substrate by a rigid flat indenter. The shear modulus of the functionally graded materials with a constant Poisson’s ratio is modeled by an exponential function which varies along the thickness direction. Both the governing equations and the boundary conditions of the receding contact problem are converted into a pair of singular integral equations using the Fourier integral transforms, which are numerically integrated by the Chebyshev–Gauss quadrature. The contact pressure and the contact size at both contact interfaces are eventually obtained iteratively, as developed from the steepest descent algorithm. Extensive parametric studies suggest that it is possible to regulate the contact pressure and contact size by constructing the top layer from a soft functionally graded material.

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“…Çömez et al. [28] considered a receding contact problem for two‐layer FG media indented by a rigid punch.…”

Section: Introductionmentioning

confidence: 99%

On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods

et al. 2022

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The frictionless double receding contact problem for two functionally graded (FG) layers pressed by a uniformly distributed load is addressed in this paper. The gradation in the layers is assumed to follow an exponential variation through the height with constant Poisson's ratios. The lower layer rests on a homogeneous half‐plane (HP). There is no adhesion between the FG layers or between the lower layer and the HP. The body forces of the FG layers and HP are ignored. First, the governing equations are reduced to a system of two singular integral equations with contact pressures and contact lengths as unknowns using Fourier transform techniques and boundary conditions. The integral equations are solved numerically using the Gauss‐Chebyshev integration formula. Then, a parametric finite element analysis is performed using the augmented contact method. Finally, the problem was extended based on the multilayer perceptron (MLP), an artificial neural network used for different problem parameters. The effects of stiffness parameters, the normalized load length, the ratio of shear moduli, the ratio of FG layer heights to the normalized contact lengths, and normalized maximum contact pressures are explored. The results of finite element analysis and the MLP approach are used to validate the normalized maximum contact pressures and contact lengths obtained from an analytical method based on elasticity theory, and finally, good agreement between these three methods results is obtained. The obtained results could help in designing multibody indentation systems with FGMs.

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Receding contact problem for two-layer functionally graded media indented by a rigid punch

Cited by 35 publications

References 34 publications

A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods

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