Elasticity of diametrically compressed micro‐fabricated woodpile lattices

Modulus–porosity relationships are invaluable to rational material design of porous and structured solids. When struts in a lattice are compressed diametrically, the mechanics is rather complex. Herein, the problem of modulus–porosity in the spirit of scaling arguments and analyses based on simple ansatz followed by variational minimization of the elastic potential energy is addressed. Using scaling arguments, a simple power law where the apparent modulus of elasticity scales quadratically with the volume fraction for diametrically compressed elastic lattices is obtained. The modulus–porosity relationship is found to be consistent with computations and laboratory experiments on additively manufactured woodpile lattices with various cross-sectional shapes and lattice spacing. It is also shown that the persistence length of diametrically pinched elastic rods is small, so that the effect of compressive strain from neighboring sites can be ignored. The decay behavior is surprisingly accurately captured by the variational approach and is consistent with computations. Finally, the range of validity of the quadratic power law presented here, up to relative density ~80%, is identified. On the apparent modulus–porosity plane, the experimental data aligns well with the power law for modulus–porosity predicted from simple analyses and finite element calculations.