Design of elastically isotropic shell lattices from anisotropic constitutive materials for additive manufacturing

Abstract

Additively manufactured elastically isotropic lattice structures are promising for lightweight structural applications. Current design methods for elastically isotropic lattice structures are mostly based on the assumption of isotropic constitutive materials. However, additive manufacturing (AM) fabricated materials generally exhibit undesired anisotropy due to the layer-by-layer construction, which requires precise material models to be incorporated in structural design framework. This work presents a design method of variable thickness triply periodic minimal surface (TPMS) shell lattices to achieve elastic isotropy from homogeneous anisotropic constitutive materials. A gradient-based optimization method which adopts the universal anisotropy index as the objective is developed to handle any orthotropic lattices, extending the widely used method based on the Zener anisotropy ratio that only suits cubic lattices. To validate the proposed design method, the transversely isotropic elasticity model of micro laser powder bed fusion (μLPBF) fabricated stainless steel 316 L (SS316L) is calibrated through tensile tests, and then incorporated into the optimization method to design elastically isotropic variable thickness N14, IWP, and P shell lattices. Compression tests results of μLPBF fabricated N14 lattices demonstrate that the proposed design reduces the relative standard deviation of the lattice’s Young’s moduli along nine directions from 0.77 (uniform thickness) to 0.75. Further numerical analysis reveals that the Young’s moduli of N14, IWP and P shell lattices along [001] direction are reduced by 2%−6% depending on the lattice type, while those along [100] and [101] directions remain almost constant after anisotropic SS316L ( E z / E x = 0.92) replaces the isotropic one. This work provides a design and analysis method for AM fabricated TPMS shell lattices made of anisotropic constitutive materials, and reveals the influences of anisotropic constitutive materials on the elastic properties of lattices.