On the Phenomenon of Separation During Compression and Frictional Sliding of an Elastic Rectangle

Abstract

The plane strain compression and sliding of an elastic rectangle is considered whose one set of parallel edges are free from tractions. The remaining set of parallel edges is simultaneously subjected by rigid rough planes to a compressive force P and a sliding force F = μP, where μ is the coefficient of sliding friction. The rigid planes are prevented from rotation and a limiting equilibrium is assumed by taking the contact shear stress to be equal to the product of the normal compressive stress with μ. It is found that the presence of free edges significantly affects the deformation of the rectangle. In particular, it is shown that during sliding the leading edge of the rectangle is compressed most severely against the rigid plane, whereas separation takes place at the trailing edge. The separation occurs at the slightest trace of the application of load and although the magnitude depends upon the level of loading, the extent of the zone depends only on Poisson’s ratio, frictional coefficient, and the aspect ratio. Numerical results of the quantities of practical interest are reported.