Continuous and discontinuous contact problem for a layered composite resting on simple supports

The frictionless contact problem for a layered composite which consists of two elastic layers<br />having different elastic constants and heights resting on two simple supports is considered. The external<br />load is applied to the layered composite through a rigid stamp. For values of the resultant compressive<br />force P acting on the stamp vertically which are less than a critical value Pcr and for small flexibility of<br />the layered composite, the continuous contact along the layer - the layer and the stamp - the layered<br />composite is maintained. However, if the flexibility of the layered composite increases and if tensile<br />tractions are not allowed on the interface, for P > Pcr, a separation may be occurred between the stamp<br />and the layered composite or two elastic layers interface along a certain finite region. The problem is<br />formulated and solved for both cases by using Theory of Elasticity and Integral Transform Technique.<br />Numerical results for Pcr, separation initiation distance, contact stresses, distances determining the<br />separation area, and the vertical displacement in the separation zone between two elastic layers are given.