Finite Element Analysis of a Layered Elastic Solid in Normal Contact With a Rigid Surface

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Abstract
Based on the finite element method, the elastic contact problem of a layered semi-infinite solid compressed by a rigid surface is solved numerically. The case of a surface layer stiffer than the substrate is considered, and general solutions for the subsurface stress and deformation fields are presented for relatively thin, intermediate, and thick layers. Additionally, the stresses in a compressed homogeneous half-space having the substrate properties have been obtained for comparison. The significance of the layer thickness relative to the size of the half-contact width, the friction coefficient at the contact zone, and the stiffness of the layer are critically examined and the conditions under which the layer is beneficial are addressed. Furthermore, the mechanisms of microcrack initiation at the layer surface or interface, layer debonding, and onset of plastic flow in the layered solid are explained qualitatively, in light of the governing stresses, and the regimes of their prevalence are approximately determined.

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