Material Properties of Planar Lattices

Lattice materials have become increasingly popular in engineering because their architecture can be tailored to achieve remarkable material properties. While the properties of regular tessellations, such as hexagonal, square, and triangular lattices, have been studied extensively, those of other promising architectures, like semi- and demi-regular lattices, have remained unexplored. Therefore, the aim of this thesis is to quantify the properties of semi- and demi-regular lattices, and compare them to existing regular architectures. The in-plane mechanical properties of seven semi-regular lattices were derived analytically. Expressions for the elastic modulus and strength under uniaxial compression and shear were developed and then verified with finite element simulations. The analysis showed that one topology is stretching-dominated; two are stretching-dominated in compression but bending-dominated in shear; and four are bending-dominated. The stretching-dominated semi-regular tessellation has a high elastic buckling strength, being 43% stronger than a regular triangular lattice. Otherwise, one of the bending-dominated topologies is 85% stiffer and 11% stronger than a hexagonal lattice. This topology would be ideal for applications requiring high stiffness and high energy absorption. The fracture toughness of six periodic planar lattices including three semi-regular, and three demi-regular lattices was investigated. The numerical simulations revealed that the fracture toughness of two semi-regular lattices scales as bar 1.5 under mode I, where the exponent of 1.5 for relative density is unique amongst planar lattices. Furthermore, the fracture toughness of one semi-regular and two demi-regular lattices scales linearly with relative density, with one outperforming a triangular lattice by 15% under mode I and 30% mode II. The third demi-regular lattice has a fracture toughness that scales with the square root of relative density and matches the remarkable toughness of the kagome lattice. A kinematic matrix analysis revealed that periodic mechanisms may be a key feature explaining their remarkable fracture toughness. The fracture toughness predicted by FE simulations was in excellent agreement with experiments performed on CT samples produced by additive manufacturing. This demonstrates that it is possible to accurately measure the fracture toughness of lattice materials even though experiments are done with significantly fewer unit cells than what is typically used in FE simulations. The results will be beneficial for the design of specimens in future experimental studies, and the development of guidelines to measure the fracture toughness of lattice materials.