Contact Problem for Half-Spaces and Elastic Cylinder with Initial (Residual) Stresses*

The contact problem of the interaction of two prestressed half-spaces with a prestressed elastic cylindrical punch without friction forces is solved in the case of unequal roots of the characteristic equation. The study is conducted in a common form for the theory of large initial (final) strains and two variants of the theory of small initial strains within the framework of the linearized theory of elasticity for an arbitrary elastic potential. The problem is solved using the Hankel transform, paired integral equations, orthogonal polynomials, and other methods of the theory of contact problems of linearized elasticity. The numerical analysis is conducted for the Treloar potential in the form of curves.