Indentation of a flat-ended cylinder over a transversely isotropic and layered half-space with imperfect interfaces

A novel approach is presented in this paper for solving the mixed boundary-value problem between a flat-ended rigid cylinder and a transversely isotropic and layered half-space. It is based on the corresponding forward solution of multiple uniform vertical loads combined with the method of superposition via the integral least square approach. The method is first verified by existing analytical and numerical solutions and then applied to transversely isotropic and layered half-spaces with thin interlayers or imperfect interfaces. It is demonstrated that the present approach to the mixed boundary-value problem is very accurate and efficient a solution with a relative error less than 1% can be achieved by using only about 6 forward calculations (i.e., 6 uniform circular loading solutions). The indentation moduli of transversely isotropic and layered half-spaces with imperfect interfaces are calculated for various equivalent imperfect interface spring models as well as the direct thin-layer model. Equivalence and difference among different interface models are analyzed based on the indentation moduli with respect to thin-layer Young's modulus and thin-layer thickness.