Design of crack-resistant two-dimensional periodic cellular materials

The resistance to macrocrack propagation in two-dimensional periodic cellular materials subjected to uniaxial remote stresses is improved by redistributing the material of the solid phase. The materials are represented by beam lattices with regular triangular or hexagonal patterns. The purpose of the design is to minimize the maximum tensile stress for all possible crack locations allowed by the material microstructure. Two design cases are considered. In the cell design case material is redistributed between the otherwise uniform elements of the repetitive cell. In the element design case the shape of identical elements is optimized. The analysis of such infinite trellis with an arbitrary macroscopic crack is enabled by an efficient exact structural analysis approach. It is shown that the fracture toughness of the triangular layout can be significantly increased by redistribution of the material between the elements with uniform cross sections while for the case of hexagonal lattice the effect is achieved mainly by using identical elements with variable thickness distribution.