Solutions of half-space and half-plane contact problems based on surface elasticity

Zhou, S.-S.; Gao, X.-L.

doi:10.1007/s00033-012-0205-0

Cited by 75 publications

(40 citation statements)

References 40 publications

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“…Figs. 4 and 5 show the nondimensional vertical displacement, μu y =ðbq 0 Þ, and vertical stress, σ yy =q 0 , using the present FE model and the analytical solutions established by Zhou and Gao [37]. It can be concluded that the present model favorably agree with the analytical solution.…”

Section: Surface Energy Effect On Homogeneous Nanostructuressupporting

confidence: 68%

“…Long and Wang [36] extended this work to handle axisymmetric indentation problem between a sphere and a half-space. Zhou and Gao [37] derived analytical solutions for half-space and half-plane contact problems using the general form of the linearized surface elasticity theory of GM model. Gao et al [38] presented a nonclassical formulation of the Boussinesq problem, in which both the residual surface stress and the surface elasticity are considered.…”

Section: Introductionmentioning

confidence: 99%

“…Non-dimensional vertical displacement at the free surface; (a) Present FE model (b) Analytical solution,[37]. Non-dimensional vertical stress component at the free surface; (a) Present FE model (b) Analytical solution,[37].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Analysis of nanoindentation of functionally graded layered bodies with surface elasticity

Attia

Mahmoud

2015

International Journal of Mechanical Sciences

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Section: Surface Energy Effect On Homogeneous Nanostructuressupporting

confidence: 68%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of nanoindentation of functionally graded layered bodies with surface elasticity

Attia

Mahmoud

2015

International Journal of Mechanical Sciences

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“…From the above-cited references in the literature, it is noted that most of these references, e.g., Zhou and Gao [28], Long et al [25] and Long and Wang [26], handled the nanocontact problem in elastic solids as a stress analysis one. In these models, the analytical contact models such as Hertz model are firstly exploited to determine the contact pressure distribution and the extent of contact length.…”

Section: Introductionmentioning

confidence: 98%

“…Pinyochotiwong et al [27] proposed a continuumbased concept in the analysis of an axisymmetric rigid frictionless indenter acting on an elastic half space with surface energy effect. Zhou and Gao [28] derived analytical solutions for the problems of an elastic half space subjected to a distributed normal force. Fourier transforms and Bessel functions were utilized in the formulation.…”

Section: Introductionmentioning

confidence: 99%

Analysis of nanocontact problems of layered viscoelastic solids with surface energy effects under different loading patterns

Rahman

Mahmoud

2015

Acta Mech

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Surface stresses have a remarkable effect on nanocontact response of layered viscoelastic solids, especially under specific loading patterns. In the framework of nonlinear viscoelastic contact mechanics, a numerical model is developed to investigate the quasistatic nanocontact response of elastically layered viscoelastic solids under different loading patterns. The developed model accounts for surface energy effects by adopting the complete Gurtin-Murdoch surface elasticity model. The Schapery's constitutive viscoelastic creep model is used for the stress, strain, and time relationships. The transient term in the creep compliance is expressed by Prony's series. Frictionless contact condition is assumed throughout the contact interface. The equilibrium contact configuration, in which the contact constraints are exactly satisfied without any need for an appropriate value for the penalty parameter, is obtained by using the Lagrange multiplier method in the framework of the Newton-Raphson procedure. The developed model is applied to study and analyze the quasistatic nanocontact response of two different problems under different loading patterns. Results show the significant effect of the type of loading pattern and its rate on the nanocontact response of elastically layered viscoelastic solids.

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Half‐space contact problem considering strain gradient and surface effects: An analytical approach

et al. 2019

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In this article, an analytical approach is proposed for the problem of an elastic halfspace under symmetrically distributed normal force with arbitrary profile including uniform pressure, Boussinesq flat-ended punch, conical punch and Hertz's spherical punch. The formulation of the work is on the basis of Mindlin's first strain gradient theory with five material length scale parameters. Also, the surface effects are taken into account using the Gurtin-Murdoch surface elasticity theory. The developed mathematical formulation is general so that it can be simply reduced to different strain gradient-based theories such as the modified versions of strain gradient and modified couple stress theories (MSGT and MCST), the simplified strain gradient theory (A-SGT), as well as the classical theory (CT). In the solution procedure, an analytical method is applied using the Fourier and Hankel transforms.In the numerical results, the effects of material length scale parameters and kind of punch on the surface displacements and stresses of the half-space are analyzed.The surface influences are also comprehensively studied. Moreover, comparisons are made between the predictions of MSGT, MCST, A-SGT and CT. This work shows that the material length scale parameters of Mindlin's first SGT play important roles in the response of half-space. Also, the presented results provide a comparison between the intensity of effects of strain gradient parameters and surface parameters. K E Y W O R D Sfourier transform, half-space contact problem, strain gradient theory, surface stress elasticity

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Solutions of half-space and half-plane contact problems based on surface elasticity

Cited by 75 publications

References 40 publications

Analysis of nanoindentation of functionally graded layered bodies with surface elasticity

Analysis of nanoindentation of functionally graded layered bodies with surface elasticity

Analysis of nanocontact problems of layered viscoelastic solids with surface energy effects under different loading patterns

Half‐space contact problem considering strain gradient and surface effects: An analytical approach

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