Numerical investigation of the initial yield surface of perforated hollow sphere structures (PHSS) in a primitive cubic pattern

This paper investigates the initial yield surface of a new type of hollow sphere structure (HSS). For this new type, the sphere shell is perforated by several holes in order to open the inner sphere volume and surface. Multi-axial tensile loading is applied to investigate the initial yield surface of perforated HSS with ideal plastic base material properties. The influence of the hole diameters and different geometries of linking elements on the initial yield surface are shown. The results are compared to classical configurations without perforation. It is shown that the initial yield surface can be represented as a cone in the principal stress coordinate system. Increasing of the hole diameter (decreasing of the average density) decreases the diameter of this cone. Compared to the changes for different hole diameters, the shape of the initial yield surface is less sensitive to the geometry of the link between two spheres. In addition, the elastic properties of PHSS, i.e. Young's modulus and Poisson's ratio, are investigated. To this end, three-dimensional finite element analysis is used to investigate primitive cubic unit cell models.