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. We propose 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 exceeds the corresponding theoretical Hashin–Shtrikman upper (HSU) bound. Accordingly, we generated three-dimensional (3D) modulus surfaces for ST TPMS lattices with different ST angles. One can generate shear deformation under uniaxial compression, to obtain an ST TPMS lattice with a negative Poisson’s ratio. Furthermore, one can use the ST method to texture the local deformation, stress distribution, and failure form by constructing a cellular mechanical metamaterial, by combining ST and non-ST (standard) unit cells in a targeted texture pattern. This design concept is not limited to TPMS lattices; one can apply the concept to other types of strut- and sheet-based lattices.

Keywords: TPMS lattice, skew transformation, deformation, anisotropy, Young's modulus