Author(s)

Liyuan Wang^*, Wei Han, Shanlin Wang, Lihong Wang, Yinping Xin

Regional Circular Economy key Laboratory of Gansu Higher Institutions; Department of Mathematics, Longqiao College of Lanzhou University of Finance and Economics, Lanzhou, China.

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.

Surface Tension, Surface Elasticity, Nano-Contact Problem, Fourier Integral Transforms Method, Triangle Distribution Force

Wang, L. , Han, W. , Wang, S. , Wang, L. and Xin, Y. (2016) Nano-Contact Problem with Surface Effects on Triangle Distribution Loading. Journal of Applied Mathematics and Physics, 4, 2047-2060. doi: 10.4236/jamp.2016.411204.