Elastic analysis of some punch problems for a layered medium

The problems of flat-ended cylindrical, quadrilateral, and triangular punches indenting a layered isotropic elastic half-space are considered. The former two are analyzed using a basis function technique, while the latter problem is analyzed via a singular integral equation. Solutions are obtained numerically. Load-deflection relations are obtained for a series of values of the ratio of Young's modulus in the layer and substrate, and for a variety of punch sizes. These solutions provide an accurate basis for the estimation of Young's modulus of thin films from the initial unloading compliance observed in indentation tests, and are specifically relevant to axisymmetric, Vicker's, and triangular indenters. The results should also be of interest in foundation engineering. © 1987.