Hypersingular integral equations and applications to porous elastic materials with periodic cracks.

In this work a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented, The first goal of the present study is the development of an efficient analytical and direct numerical collocation method. The second one is the application of the method to the porous elastic materials when a periodic array of co-planar cracks is present. Starting from Cowin-Nunziato model and by applying Fourier integral transform the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. We also study stress-concentration factor, and investigate its behaviour versus Porosity of the material.