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Analysis of hard coatings on a substrate containing inhomogeneities

“…So far, few investigations have been conducted on inhomogeneities in a half-space. These studies include a circular rigid disc [Hunter and Gamblen 1974;Selvadurai 2001], an ellipsoidal inhomogeneity [Tsuchida and Mura 1983], a hemispheroidal inhomogeneity [Kouris and Mura 1989], a spheroidal inhomogeneity [Tsuchida et al 2000], two concentric spherical inhomogeneities [Molchanov et al 2002], and one or multiple two-dimensional arbitrarily shaped inhomogeneities [Kuo 2007;2008] The boundary element method was used in these last two works, while the Papkovich-Neuber or the Boussinesq displacement potential was used to solve the problems in the other referred works. Studies were also performed on a single or multiple inhomogeneities in one of two joining half-surfaces of dissimilar materials, e.g., [Meguid and Zhu 1995;Yu and Kuang 2003;Brusselaars et al 2007].…”