A new algorithm for computing the indentation of a rigid body of arbitrary shape on a viscoelastic half-space

In this paper the contact problem between a rigid indenter of arbitrary shape and a viscoelastic half-space is considered. Under the action of a normal force the penetration of the indenter and the distribution of contact pressure change. We wish to find the relations which link the pressure distribution, the resultant force on the indenter and the penetration on the assumption that the surfaces are frictionless. For indenters of arbitrary shape the problem may be solved numerically by using the Matrix Inversion Method (MIM), extended to viscoelastic case. In this method the boundary conditions are satisfied exactly at specified “matching points” (the mid-points of the boundary elements). It can be validated by comparing the numerical results to the analytic solutions in cases of a spherical asperity (loading and unloading) and a conical asperity (loading only). Finally, the method was implemented for a finite cylindrical shape with its curved face indenting the surface of the half-space. This last example shows the efficiency of the method in case of a prescribed penetration as well as a given normal load history.