On the contact problem on an anisotropic composite layer with a stamp in the shape of an obtuse wedge

In this paper, for the first time, an exact solution is constructed to the contact problem of the action of a rigid wedge-shaped die with an obtuse angle on a layer of composite material having arbitrary anisotropy. The study is based on the application of the exact solution of the two-dimensional Wiener-Hopfi integral equation for a wedge-shaped die with a right angle, previously constructed by the block element method. This made it possible, thanks to the homeomorphism of stamp carriers as topological spaces, to construct exact solutions to contact problems for wedge-shaped, obtuse-angled stamps. In comparison with strip stamps, the solution contains an additively additional term describing the concentration of contact stresses at the corner point, that is, at the top of the stamp. The calculation of the characteristic of the contact stress concentration at this point is close to the values obtained by approximate numerical methods in a number of studies. In the area considered away from the top of the stamp, the exact solution becomes the solution for the case of a semi-infinite stamp. The developed method is applicable to composites of arbitrary anisotropies occurring in linearly elastic materials and crystals of any cross-section. It can be useful in engineering practice and in seismology in assessing contact stress concentrations in zones of lithospheric plates having similar angles.