Stress concentration tensor for a stretchable elastic isotropic plane being weaken by a grid of isotropic elliptic inclusions

This work presents the construction of a solution to the plane doubly periodic loading problem for an infinite elastic isotropic plane with elliptical inclusions. The plane is under one of three loads: it is stretched in the direction of one of the inclusion axes or it has a pure shear at infinity. The concept of stress concentration tensor is considered and an example of its construction is shown. The solution of the problem is reduced to the search for complex functions from the boundary conditions obtained from the equality of displacements and normal forces of the matrix and inclusions using conformal mappings and integration by the Muskhelishvili method. The effect of non-central inclusions is expressed by using the small parameter method.