Stress concentration localization in doubly periodic square systems of circular holes in uniaxial compression

Abstract

We consider the stress concentration points in infinite elastic doubly periodic perforated plates (lattices) under the conditions of external uniaxial compression. Special attention is paid to the internal localization of stress concentrations (i.e., to the case of stress concentration origination inside the material rather than on the boundaries of the holes). We consider a parametric domain (depending on the angle of application of the external load and the structure parameter of the lattice) and calculate the domain dimensions (the extreme values of the parameters). We discover a point in the parametric domain at which the following three cases of fracture initiation are possible: two cases on the hole contour and one case inside the material.