Tailoring Compressive Stiffness of Additively-Fabricated Lattice Materials

Design of architectured materials is greatly facilitated by simple rules that relate structure to their apparent properties. Analytical expressions for modulus-porosity relationships, when possible, are thus invaluable to rational material design. When the struts in a remotely loaded micro-fabricated woodpile lattice are compressed diametrically, the mechanics of such structures is not simple. Here we show that the apparent modulus of elasticity of such porous lattices depends quadratically on the volume fraction for such diametrically compressed lattices. This power law could be key to material design of a host of additively manufactured lattice materials. We first obtain a novel power law using a simple scaling argument. The modulus-porosity relationship is then found to be consistent with our computations and laboratory experiments on additively manufactured lattices with various cross-sectional shapes and lattice spacing. We also show that the persistence length of diametrically pinched elastic rods is small, so that the effect of compressive strain from neighbouring sites can be ignored. Finally, we identify the range of validity of the quadratic power law presented here-it is up to relative density∼ 80%.