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An analytical solution of adhesion contact for a rigid sinusoidal surface on a semi-infinite elastic body is presented. The solution for an equilibrium condition of the system for a combination of the work of Johnson [International Journal of Solids and Structures, 32(3–4), pp. 423–430, 1995] and Zilberman and Persson [Solid State Communications, 123(3–4), pp. 173–177, 2002; Journal of Chemical Physics, 118(14), pp. 6473–6480, 2003] under zero external pressure is obtained. The interfacial term of the total energy is calculated by considering the curvature of the contact area following the approach of Zilberman and Persson rather than the straight line of the contact area as Johnson. Our results agree with both the analytical result of Johnson for a slightly wavy surface and the numerical results of Zilberman and Persson for a largely wavy surface at the limitations of their assumptions. The equilibrium contact width is clearly expressed and the effect of the surface roughness is discussed.

Analytical solution of adhesion contact for a rigid sinusoidal surface on a semi-infinite elastic body