Inverse analysis for evaluation of the shear modulus of inhomogeneous media by torsion experiments

The present paper addresses the problem on torsion of a circular indentor with a flat base on a half-space covered by an inhomogeneous coating with shear modulus arbitrarily varying in-depth. Approximate analytical solution of this problem is developed. The obtained formulas allow one to determine the distribution of contact stresses under indentor, as well as the dependence of the torsion moment applied to the indentor from the twisting. It is shown that the approximate formulas are asymptotically exact both at large and small values of characteristic dimensionless geometrical parameter of the problem.Based on the analysis of the derived solution, we suggest evaluation technique for the shear modulus of a functionally-graded coating in the case when it depends on one parameter only. The technique uses the data received in the course of torsion experiments by a series of indentors of various radii.