Anisotropy and deformation of triply periodic minimal surface based lattices with skew transformation

Abstract

Triply periodic minimal surfaces (TPMSs) are common in energy, aerospace, optics, and medical fields. Although many works focus on substantially tuning the anisotropy for a hybrid lattice with various TPMS types, tuning the anisotropy for a single TPMS type has not been sufficiently investigated. This study proposes a skew transformation (ST) to distort TPMS lattices at the design stage, to modify their mechanical anisotropies and tailor their deformations under uniaxial loading. The ST method enables a standard TPMS lattice to increase the direction-dependent modulus without changing the lattice’s volume fraction, which is 38% higher than the theoretical Hashin–Shtrikman upper (HSU) bound for a sheet lattice. Accordingly, three-dimensional (3D) modulus surfaces were generated for ST lattices with different ST angles. Shear deformation under uniaxial compression was generated to obtain a nominal negative Poisson’s ratio of −0.66 with the combination of ST and hole design. Furthermore, the ST method was used to texture the local deformation, stress distribution, and failure form by constructing a cellular mechanical metamaterial, by combining ST and standard unit cells in a targeted texture pattern. This design concept is not limited to TPMS lattices and can be applied to other types of strut- and sheet-based lattices.