An Axisymmetric Problem of a Disc-shaped Rigid Inclusion in an Elastic Layer with Smoothly Clamped Boundaries

An axisymmetric deformation of an elastic layer due to the indentation of a penny-shaped crack by a disc-shaped rigid inclusion in its middle plane was studied. The two surfaces of the thick layer are supposed to be smoothly clamped. Using the Hankel integral transforms method, we reduced the three-part mixed boundary value problem to a system of triple integral equation. With the help of the Gegenbauer formula and some integral representations of the Bessel function, we get an infinite system of algebraic equation for determining the unknown function. The expression of the stress intensity factors was given analytically. Some quantities of physical interest were shown graphically followed by a discussion of the effect of the radii of the inclusion and the crack as well as the thickness medium on the layer deformation.