Elastically-isotropic open-cell minimal surface shell lattices with superior stiffness via variable thickness design

Triply periodic minimal surface (TPMS) shell lattices are attracting increasingly attention due to their unique combination of geometric and mechanical properties, and their open-cell topology. However, uniform thickness TPMS shell lattices are usually anisotropic in stiffness, namely having different Young's moduli along different lattice directions. To reduce the elastic anisotropy, we propose a family of variable thickness TPMS shell lattices with isotropic stiffness designed by a strain energy-based optimization algorithm. The optimization results show that all the six selected types of TPMS lattices can be made to achieve isotropic stiffness by varying the shell thickness, among which N14 can maintain over 90% of the Hashin-Shtrikman upper bound of bulk modulus. All the optimized shell lattices exhibit superior stiffness properties and significantly outperform elastically-isotropic truss lattices of equal relative densities. Both uniform and optimized types of N14 shell lattices along [100], [110] and [111] directions are fabricated by the micro laser powder bed fusion techniques with stainless steel 316 L and tested under quasi-static compression loads. Experimental results show that the elastic anisotropy of the optimized N14 lattices is reduced compared to that of the uniform ones. Large deformation compression results reveal different failure deformation behaviors along different directions. The [100] direction shows a layer-by-layer plastic buckling failure mode, while the failures along [110] and [111] directions are related to the shear deformation. The optimized N14 lattices possess a reduced anisotropy of plateau stresses and can even attain nearly isotropic energy absorption capacity.