RESEARCH ARTICLEZheng-Dong MAMacro-architectured cellular materials: Properties,characteristic modes, and prediction methods© Higher Education Press and Springer-Verlag GmbH Germany 2018Abstract Macro-architectured cellular (MAC) materialis def i ned as a class of engineered materials havingconf i gurable cells of relatively large (i.e., visible) size thatcan be architecturally designed to achieve various desiredmaterial properties. Two types of novel MAC materials,negative Poisson’s ratio material and biomimetic tendonreinforced material, were introduced in this study. Toestimate the effective material properties for structuralanalyses and to optimally design such materials, a set ofsuitable homogenization methods was developed thatprovided an effective means for the multiscale modelingof MAC materials. First, a strain-based homogenizationmethod was developed using an approach that separatedthe strain f i eld into a homogenized strain f i eld and a strainvariation f i eld in the local cellular domain superposed onthe homogenized strain f i eld. The principle of virtualdisplacements for the relationship between the strainvariation f i eld and the homogenized strain f i eld was thenused to condense the strain variation f i eld onto thehomogenized strain f i eld. The new method was thenextended to a stress-based homogenization process basedon the principle of virtual forces and further applied toaddress the discrete systems represented by the beam orframe structures of the aforementioned MAC materials.The characteristic modes and the stress recovery processused to predict the stress distribution inside the cellulardomain and thus determine the material strengths andfailures at the local level are also discussed.Keywords architectured material, cellular materials,multi-scale modeling, homogenization method, effectivematerial properties, computational method1 Introduction1.1 Tendency of the new material developmentLightweight materials have become a critical requirementfor reducing the weight of automotive and aerospacevehicles to achieve better fuel eff i ciency, lower emissions,and improved environmental protection. Parallel to theeffort of improving the strength of traditional metalmaterials, new materials, such as f i ber-reinforced compo-sites, foams, lattice, and sandwich materials have beendeveloped to expand the boundaries of the materialproperty space def i ned by traditional solid materials.Important features in these new materials include 1)using two or more raw materials in a composition to form anew material, and 2) introducing porosity into solidmaterials. The use of two or more raw materials in acomposite makes it possible to make the best use of theunique properties of raw materials and to compensate fortheir weaknesses. For example, f i ber materials usuallyhave very high tension strength but have no compressionresistance. By composting f i ber materials, e.g., carbonf i ber with a matrix material such as resin, the weakness ofthe f i ber can be overcome. However, introducing porosityin a composite material usually can further improve thebending stiffness (and other features) of the resultingstructure and reduce the weight signif i cantly. These newmaterials are artif i cially made and usually have a cellularstructure with some kind of architecture within thecharacteristic cells; therefore, they are called “architecturedcellular materials” in this study [1].In our opinion, there are two opposite tendencies in thedevelopment of architectured materials: One tendency is toreduce the scale of the materials, i.e., by having smallercells, and the other is increase it. Nowadays, researchershave been able to fabricate new materials in very smallscales, such as nano and atomic scales. As shown on theleft side of Fig. 1, graphene, nanotube, and micro-trusseshave been developed. These kinds of materials are calledmicro-architectured materials [2]. Even though micro-Received May 7, 2017; accepted August 14, 2017Zheng-Dong MA ( ? )The University of Michigan, Ann Arbor, MI 48109, USAE-mail: mazd@umich.eduFront. Mech. Eng.https://doi.org/10.1007/s11465-018-0488-8
