A new numerical approach for the contact analysis between a spherical nanoindenter on the surface of viscoelastic half-space

Boundary value problems involving contact are great importance in industries related to mechanical and civil engineering، also in environmental، medical، military and aerospace applications. In this paper، the nanoindentation contact problem between a rigid spherical indenter and surface of a viscoelastic half-space of arbitrary shape is considered under assumption of interfacial surfaces are frictionless. Deriving of the relations between the contact pressure distribution، the resultant force on the indenter and the penetration on viscoelastic surface is the main scope of presented study. By appropriate formulation of the viscoelastic constitutive equations، the problem can be solved numerically using the Matrix Inversion Method (MIM)، extended to viscoelastic indentation case and with exactly satisfying the boundary conditions. Comparison of the numerical results with analytical ones for loading-unloading procedure of spherical indenters، shows the efficiency of the method in case of a prescribed penetration as well as given load history.