Fast numerical method for crack problem in the porous elastic material

The present paper discusses the crack problem in the linear porous elastic plane using the model developed by Nunziato and Cowin. With the help of Fourier transform the problem is reduced to an integral equation over the boundary of the crack. Some analytical transformations are applied to calculate the kernel of the integral equation in its explicit form. We perform a numerical collocation technique to solve the derived hyper-singular integral equation. Due to convolution type of the kernel, we apply, at each iteration step, the classical iterative conjugate gradient method in combination with the Fast Fourier technique to solve the problem in almost linear time. There are presented some numerical examples for materials of various values of porosity.