Analytical design of stretching-dominated truss lattices with tailored elasticity from transversely isotropic base materials

Abstract

Incorporating the process-induced material anisotropy into design framework of additively manufac-tured lattice structures is crucial to ensure the accuracy of design and analysis models. This work pro-poses an analytical approach to design stretching-dominated truss lattices with tailored elastic properties, including isotropic elasticity, tailored zero/negative Poisson's ratios, tailored Young's moduli ratios along specified directions. The transversely isotropic elasticity is adopted to represent the micro lase powder bed fusion (LPBF) process-induced anisotropy of base materials. The lattices are designed through combination of elementary bars with appropriate volume fractions. An analytical homogeniza-tion theory is established to determine elastic constants of combined lattices. An analytical design approach is proposed to obtain elastically isotropic truss lattices. A traversal searching is performed to determine ranges of Young's moduli, Poisson's ratios of combined lattices, and find most manufacturable ones with tailored Young's moduli ratios and Poisson's ratios. Finite element analysis reveals all designed lattices from anisotropic materials achieve better agreements to design targets than those designed from isotropic materials, thus validating the superiority of the proposed method. The lattices with isotropic elasticity, tailored zero/negative Poisson's ratios are fabricated in stainless steel 316L via micro-LPBF, and quasi-static compression experiments are performed to further validate the proposed design approach.