A Computational Matrix Inversion Approach for Analysis of Contact Problems between any Rigid Nano-indenter and Viscoelastic Bodies

In this paper، the procedure of a novel computational solution for the formulation and analysis of nano-indentation contact problems between a viscoelastic half-space and a rigid indenter of any arbitrary geometry is presented. The main objective of this paper is to develop the relations which link the contact pressure distribution، the load on the indenter، and the indentation depth with assumption that the surfaces are frictionless. The viscoelastic indentation problem has been solved numerically employing a proper formulation in constitutive equations and applying a new matrix inversion approach satisfying the boundary conditions. The computational approach has been validated by comparing the numerical results to the analytic ones for loading and unloading process of a spherical nano-indenter.