Design of isotropic porous plates for use in hierarchical plate-lattices

Abstract

This work deals with the elastic and plastic properties of two-dimensional periodic metamaterials. Design maps are developed to ensure their isotropic elastic response while attaining the theoretical stiffness limits. Numerical simulations of two different topologies - triangular and round hole staggered patterns - are performed to analyze their large deformation response for relative densities ranging from 0.1 to 0.9. The investigations show that the strength of triangular perforated plates is profoundly dependent on the unit cells’ direction concerning the axial loading; 0 and 30 degrees have the lowest and highest yield strength over the entire range of volume fractions. In contrast, the round hole staggered patterns exhibit an almost uniform yield strength in all directions. The yield strength of the circular patterns is significantly lower at low- and intermediate-density ranges; whereas they outperform the triangular ones at relative densities higher than 0.6. Additionally, validation experiments are performed on specimens of 0.3 relative density that have been extracted from DP980 steel sheets using micro waterjet cutting, showing good agreement in terms of force-displacement response and surface strain fields. A foam-like structure is built from periodic sheets and the scaling of the elastic properties of the resulting hierarchical 3D metamaterial are discussed.