Optimal lattice-structured materials

Abstract

This work describes a method for optimizing the mesostructure of lattice-structured materials. These materials are periodic arrays of slender members, resembling efficient, lightweight macroscale structures like bridges and frame buildings. Current additive manufacturing technologies can assemble lattice structures with length scales ranging from nanometers to millimeters. Previous work demonstrates lattice materials have excellent stiffness-and strength-to-weight scaling, outperforming natural materials. However, there are currently no methods for producing optimal mesostructures that consider the full space of possible 3D lattice topologies. The inverse homogenization approach for optimizing the periodic structure of lattice materials requires a parameterized, homogenized material model describing the response of an arbitrary structure. This work develops such a model, starting with a method for describing the long-wavelength, macroscale deformation of an arbitrary lattice. The work combines the homogenized model with a parameterized description of the total design space to generate a parameterized model. Finally, the work describes an optimization method capable of producing optimal mesostructures. Several examples demonstrate the optimization method. One of these examples produces an elastically isotropic, maximally stiff structure, here called the isotruss, that arguably outperforms the anisotropic octet truss topology.

Numerically-aided 3D printed random isotropic porous materials approaching the Hashin-Shtrikman bounds

“…These microstructures has been shown so far to deliver rather optimal mechanical properties in some specific directions due to the microstructural symmetries and under specific loads. In this context, Messner (2016), Meza et al (2017) and Tancogne-Dejean and Mohr (2017) have recently designed almost-isotropic elastic microstructures by imposing a group of constraints on lattice truss networks. The resulting lattices were shown to lead to a fixed overall Poisson's ratio and a fixed relative effective Young's Modulus for a given porosity which is found in many cases to be relatively far from the upper Hashin-Shtrikman bounds.…”

Old materials - new capabilities: lattice materials in structural mechanics

“…• maximisation (Messner, 2016;Bauer et al,2016) • tuning (for reproduction of human bone stiffness) (Serra-Garcia et al, 2016)…”

“…However, spatial variation of the cell type and beam diameters is intuitionally beneficial, and has been suggested by some authors (e.g. Messner, 2016). Some simple solutions can be directly borrowed from the classic design rules, e.g.…”

Multiobjective optimization of modular structures: Weight versus geometric versatility in a Truss‐Z system

“…Certain analogues can be also found in the area of multiscale (and often multiphysical) material modeling with representative volume elements (RVE) used at the microscale level (Wang, Luo, Zhang, & Qin, 2016;Chen, Zhou, & Li, 2010;Chen, Yu, Xia, Liu, & Ma, 2017) or latticestructured materials with mesoscale cells (Messner, 2016;Augustyniak, 2018). However, typical optimization objectives express selected properties of the homogenized material itself, and they usually do not involve global-level properties as typical in structural optimization and structural mechanics.…”