Effects of surface tension on axisymmetric Hertzian contact problem

Long, Jianmin; Wang, Gangfeng

doi:10.1016/j.mechmat.2012.09.003

Cited by 74 publications

(58 citation statements)

References 27 publications

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“…Long et al [25] formulated the indentation of a 3D contact problem between a sphere and a half space with surface tension. This work was extended by Long and Wang [26] who considered the axisymmetric contact between a rigid sphere and an elastic half space. 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.…”

Section: Introductionmentioning

confidence: 99%

“…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: 99%

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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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Section: Introductionmentioning

confidence: 99%

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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“…Wang et al [12] studied the response of a halfplane subjected to normal pressures with constant residual surface tension. Long and Wang [13] studied the effect of the residual surface stress on the two dimensional Hertz contact problem, and later Long et al [14] generalized their work to the three dimensional case. Wang [15] derived the general analytical solution of nano-contact problem with surface effects by using the complex variable function method.…”

Section: Introductionmentioning

confidence: 99%

Effect of Surface Tension on Nanocontact Problem

Wang¹

2017

Proceedings of the 2017 International Conference on Applied Mathematics, Modeling and Simulation (AMMS 2017)

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Abstract-This paper proposes an application of surface elasticity theory in the analysis of contact problem at nano-scale. The Fourier integral transform method is adopted to derive the fundamental solutions for contact problem with surface tension effects. As a special case, the deformation induced by normal triangle distribution force is discussed in detail. The results indicate some interesting characteristics in nano-mechanics, which are distinctly different from those in classical contact problem. The results show that the hardness of material depends strongly on the surface tension.

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“…Long and Wang [17] studied the effect of the residual surface stress on the two dimensional Hertz contact problem, and later Long et al [18] generalized their work to the three dimensional case. Wang [19] derived the general analytical solution of nano-contact problem with surface effects by using the complex variable function method.…”

Section: Introductionmentioning

confidence: 99%

Nano-Contact Problem with Surface Effects on Triangle Distribution Loading

Wang¹,

Han²,

Wang³

et al. 2016

JAMP

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This work presents a theoretical study of contact problem. The Fourier integral transform method based on the surface elasticity theory is adopted to derive the fundamental solution for the contact problem with surface effects, in which both the surface tension and the surface elasticity are considered. As a special case, the deformation induced by a triangle distribution force is discussed in detail. The results are compared with those of the classical contact problem. At nano-scale, the contributions of the surface tension and the surface elasticity to the stress and displacement are not equal at the contact surface. The surface tension plays a major role to the normal stress, whereas the shear stress is mainly affected by the surface elasticity. In addition, the hardness of material depends strongly on the surface effects. This study is helpful to characterize and measure the mechanical properties of soft materials through nanoindentation.

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Effects of surface tension on axisymmetric Hertzian contact problem

Cited by 74 publications

References 27 publications

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

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

Effect of Surface Tension on Nanocontact Problem

Nano-Contact Problem with Surface Effects on Triangle Distribution Loading

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