Isotropic cellular structure design strategies based on triply periodic minimal surfaces

Isotropy is a desired characteristic in cellular structures for load bearing and energy absorption applications that must respond uniformly under external loads in all orientations. Triply periodic minimal surface (TPMS) cellular structures are attracting much attention for such applications due to their demonstrated high performance, tailorable properties, and open cell architecture. However, TPMS structures usually display stiffness anisotropy. In this work, new design strategies are presented for isotropic TPMS-based cellular structures, revealing a large available design space in terms of relative density and relative stiffness. The first design strategy arranges TPMSbased cells in a Simple-Cubic/Face-Centred Cubic inspired pattern, resulting in reduced elastic anisotropy. Two parametric optimisation approaches involving level-set mid-surface offsetting and the functional grading of relative density are then applied in a second step to eliminate any residual elastic anisotropy. Anisotropy is characterised through finite element analysis using the Zener ratio. Four families of cells are optimised, each based on a different TPMS unit cell, and then additively manufactured using the material extrusion process with polylactic acid. Finally, experimental quasi-static compressive tests are conducted to characterise stiffness, strength, and energy absorption properties. Optimised designs are tested in three crystal orientations ([001], [101] and [111]) and manufactured in three orthogonal print orientations. The Primitive TPMS-based design is the stiffest of the four designs reaching 64.4% of the Hashin-Shtrikman upper bound of bulk modulus at 20% relative density. Experimental results validate all four optimised cell designs for elastic isotropy and indicate that all the cell designs are also isotropic in terms of crushing strength and energy absorption.