Indentation of an Absolutely Rigid Thin Inclusion into One of the Crack Faces in an Elastic Plane Under Slippage at the Ends

Abstract

AbstractThe article considers the stress state of an elastic plane with a crack of finite length, when an absolutely rigid thin inclusion of the same length is pressed into one of edges, under the action of a concentrated force. For the contacting side of the inclusion, it is assumed that in its middle part, there is adhesion to the matrix, and slippage occurs along the edges, which is described by the law of dry friction. The problem is mathematically formulated as a system of singular integral equations, the behavior of the unknown functions in the vicinity of the ends of the inclusion-crack and at the separation points of the adhesion and slip zones is studied. The governing system of integral equations is solved by the method of mechanical quadratures. The laws of distribution of contact stresses, as well as the lengths of the adhesion and slip zones, depending on the coefficient of friction, Poisson’s ratio of the half-plane material, and the angle of inclination of the external force, are found.KeywordsElasticityMixed boundary value problemThin inclusionCrackContact modelAdhesion and slip zonesQuadrature rules