Effective stiffness, strength, buckling and anisotropy of foams based on nine unique triple periodic minimal surfaces

Abstract

Recent advancements in the field of additive manufacturing has led to an increased interest in the study of cellular architectures especially triply periodic minimal surfaces (TPMS) and their properties. In this study, 9 sheet-based TPMS architectures are studied by comparing their effective stiffness, strength, buckling and anisotropic properties. The TPMS lattices are generated using level set equations where the relative density of each lattice is varied to study the effective properties as a function of relative density. Finite element models of these lattices are built to study the elastic and plastic deformation behaviour under uniaxial, shear, hydrostatic and buckling loading conditions. Effective properties such as Young’s modulus, shear modulus, bulk modulus, Poisson’s ratio and strengths under uniaxial, shear, hydrostatic and buckling loading are computed against each other and other common lattice structures. In addition, anisotropic behaviour as well as the orientation dependence of the properties of each lattice are also studied. The geometric efficiency criterion is predominantly used to evaluate the different structures and the results obtained are consolidated in both quantitative and qualitative manner. SC lattice outperforms all the other lattices in terms of strength and stiffness efficiencies at lower and higher relative densities. On the other hand, I2 − Y** lattice shows the weakest stiffness and strength efficiency especially at higher relative densities. The current study focuses on the properties of some unique lattice architectures that have not been studied previously and shows promising efficiencies compared to the common architectures studied such as the Gyroid lattice. This study opens the door for employing these lattices in various applications and the results are very useful to multi-scale topology-optimization studies.