Anisotropy and deformation of triply periodic minimal surface based lattices with skew transformation - Yang, Nan; Qian, Zheng; Wei, Huaxian; Zhao, Miao (Materials & design, 2023)
[Display omitted] •Skew transformation (ST) was applied to modify standard lattices with constant volume fraction.•The maximum direction-dependent Young’s modulus of the ST lattice can approach or exceed the Hashin–Shtrikman upper bound.•ST was used to guide structural shear deformation and create a hybrid lattice with a nominal negative Poisson’s ratio.•Stress and failure patterns were textured in hybrid structures that consist of ST and non-ST units. 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.