Two-dimensional Hertzian contact problem with surface tension

Long, Jianmin; Wang, Gangfeng; Feng, Xi‐Qiao; Yu, Shou-Wen

doi:10.1016/j.ijsolstr.2012.03.017

Cited by 58 publications

(45 citation statements)

References 31 publications

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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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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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“…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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“…Zhao and Rajapakse [16] studied the 2D plane and axisymmetric surface loading problems of an elastic layer without imposing any restrictions on the surface properties. Long et al [35] considered a 2D Hertzian indentation problem between a cylinder and a half space with surface tension by neglecting the surface elasticity. Long and Wang [36] extended this work to handle axisymmetric indentation problem between a sphere and a half-space.…”

Section: Introductionmentioning

confidence: 99%