# Mathematical modeling of the contact interaction of two elastic transversely isotropic half-spaces, one of which contains a near-surface groove of an elliptical section

## DOI:

https://doi.org/10.20535/SRIT.2308-8893.2022.1.09## Keywords:

mathematical modeling, transversely isotropic half-space, near-surface groove, elliptical section, parameters of contact interaction## Abstract

On the basis of a mathematical model, the problem of compression of two elastic transversely isotropic half-spaces, one of which contains a shallow near-surface groove of an elliptical section, is considered. The solution to the problem is obtained using the Elliott representation for a transversely isotropic body in terms of harmonic functions, classical harmonic potentials and reducing the boundary value problem to considering an integro-differential equation with an unknown domain of integration. As a special case, the obtained analytical expressions yield the basic parameters of the contact of transversely isotropic half-spaces in the presence of an axisymmetric groove in one of them, as well as the parameters of the contact interaction of two elastic isotropic half-spaces, one of which contains an elliptical cross-section groove. Numerical results are obtained, the influence of elastic properties of half-spaces, geometrical parameters of groove and loading on contact interaction and closing of the gap between bodies is studied.

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