On The Bergman Operator Method and Anti-Plane Contact Problems Involving an Inhomogeneous Half-Space

A formal solution to the equation governing antiplane deformations of inhomogeneous elastic materials is presented. The solution is used to consider particular contact problems for an inhomogeneous half-space in which the shear modulus adopts the form $\mu = ( {\alpha y + \beta } )^2 $ where $\alpha $ and $\beta $ are constants.