Partial closure of the periodic system of variable width bridged slits in an isotropic medium under compression

Abstract

The problem of compression of an isotropic medium by a periodic system of variable width slits comparable with elastic deformations is considered. The slit faces are under internal pressure. It is considered that the slits have end zones wherein material's tractions act. It is accepted that interaction of the slit's surface under applied loads may reduce the formation of contact zones of their surfaces. The formation of several contact areas of faces of each slit is studied. Therewith, it is considered that on some parts of a contact area there happens stick of the faces, on the remaining part there may happen slippage. The problem of equilibrium of a periodic system of slits with partially contacting faces under compressing load is reduced to the problem of linear conjugation of analytic functions. Determination of unknown parameters characterizing partial closing of a periodic system of variable width slits is reduced to the solution of the system of singular integro-differential equations. The contact stresses, the tractions in bonds between the slit faces in the end zones, the sizes of the contact areas, the adhesion and end zones are studied.