Diagonal

Anisotropy

Poisson's ratio

Shear modulus

Statistics

Materials science

Poisson distribution

Polymer

Physics

Mathematics

Optics

Copolymer

Elastic modulus

Geometry

Composite material

Modulus

Gyroid

Materials & Design

Unlike random cellular materials, in TPMS structures the ligament size and orientation distribution are constant, leading to a directional dependency of the mechanical properties. In this work, the directional dependency of elastic properties of seven TPMS-based structures has been studied in a wide range of the solid phase volume fractions (i.e., 10–90%). Our study indicates that the strong and weak directions in IWP, Gyroid, FRD, FKS, and Diamond are diagonal and axial, respectively. In contrast, Schwarz-P and Neovius structure show a reversed order. Then, the idea of designing hybrid structures consisting from Schwarz-P/Neovius and each of the other five structures in laminated or matrix-spherical inclusion form has been employed to obtain structures with a more uniform directional elastic modulus. First, the mathematical functions of the hybrid structures are presented. The functions are carefully parameterized to ensure a smooth transition between two structures. Then the effect of the combination ratio of the parent structures on the universal anisotropy index of the hybrid structures is investigated. Our study indicates that hybrid structures have more uniform directional elastic modulus compared to their parent structures, and an appropriate selection of the combination ratio of the parent structures can lead to the least universal anisotropy.

On the directional elastic modulus of the TPMS structures and a novel hybridization method to control anisotropy