“…Recently, surface effect in contact mechanics attracts many interests, including the Boussinesq problem Zhou and Gao, 2013 ), the Cerruti problem Zhou and Gao, 2014 ) and the plane strain or axisymmetric model of indenters with different shapes contacting an elastic substrate or a layer-substrate system ( Long et al, 2012;Long and Wang, 2013;Pinyochotiwong et al, 2013;Zhou and Gao, 2013;Rungamornrat et al, 2016;Tirapat et al, 2017 ). Compared with the classical contact model ( Johnson, 1987 ), additional surface-induced tractions as a function of surface stress are introduced at the contact surface, which depends not only on the surface residual stress resulted from surface relaxation but also on the surface deformation yielded by the external load, i.e., σ s = τ 0 I + C s : ε s .…”