High stiffness topology optimised lattice structures with increased toughness by porosity constraints

[Display omitted] •Topology optimisation for high stiffness with constrained porosity.•New functionally graded tetrahedral lattice structure mapped to relative density field.•Tailored porosity can impart high residual toughness and maintain high stiffness. The stiffness and toughness of topology optimised structures containing lattices under three-point bending is studied. A porosity constraint is introduced to control the proportion of lattice generated while optimising the beams for minimum compliance. A novel tetrahedron element-based lattice with tapered trusses and a near-isotropic elastic response is developed to accurately map the relative densities from topology optimisation to a 3D printable structure. Topology optimised solid structures (0 % porosity), used for benchmarking, are found to have high stiffness but can be susceptible to buckling. At the other extreme, structures comprising entirely of lattice (100 % porosity) are shown to have low initial stiffness and low residual toughness. An experimental parametric study reveals that porosity can be tailored between these two bounds to achieve both high stiffness and high residual toughness.