Some Boundary Value Problems of Elastic Media Containing Rigid Inclusions Under Compressive Mechanical Loads

In this work we discuss some 2D boundary-value problems related to an elastic medium containing a thin rigid inclusion with general geometrical shape located in the interface between two separate elastic half-planes and subjected to compressive loading. Assuming perfect bonding between the inclusion and elastic medium, Fourier and Henkel integral transformation techniques are used to obtain the exact solution for the problem. Explicit forms are presented for arbitrary forms of thin inclusions, demonstrating that the tangent shear stress at the end-points of the inclusion has a square-root singularity. It is also shown that the normal stress has a logarithmic singularity when the end-points of the inclusion are approached from the inside of the inclusion and a square-root singularity when the end-points of the inclusion are approached from the outside of the inclusion. For special, extreme cases the solutions for anti-cracks are also presented.