A Multiscale Approach to Assess the Effect of Multilevel Structuring on the Properties of Hierarchical Lattice Materials
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A Multiscale Approach to Assess the Effect of Multilevel Structuring on the Properties of Hierarchical Lattice Materials Andrea Vigliotti1 and Damiano Pasini1 1 Department of Mechanical Engineering - McGill University 817 Sherbrooke Street West, Montreal, QC ABSTRACT Natural materials have often a defined multilevel hierarchy which governs their macroscopic mechanical properties. Cork, sponge and bone are only a few examples. These materials are generally heterogeneous and can exhibit a cellular pattern, i.e. a partition of a solid with voids, at multiple levels of the structural hierarchy. It is well known that the arrangement of the voids plays a major role in the overall performance of the material. Furthermore, it has been demonstrated that the nesting of cellular patterns at different levels confers remarkable mechanical properties to the structure. This paper presents a multiscale approach to the analysis of a hierarchical structure which exhibits nested levels of lattice, i.e. regular periodic patterns of voids occur at different length scales. A number of three-dimensional topologies as well as the effect of lattice geometry parameters have been investigated. The results of the analysis are plotted onto material property charts. The visualization of the properties helps gain insight into the contribution that each hierarchical layer imparts to the overall properties of a component hierarchically structured with lattice materials. INTRODUCTION Materials with defined levels of structural hierarchy are widespread in Nature. Bone, wood, seashells and muscular tissues, are only a few examples of biological materials displaying multiple layers of structural organization. At the macroscopic scale, several of them exhibit cellular patterns, characterised by a large abundance of voids and channels that allows them to perform multifunctional tasks. Their cell walls, at a closer look, might present further cellular structure, which can be nested at more than one level. Wood, for example, is a cellular solid consisting mainly of hollow tubes; the cell wall in turn has its own structure, which can be regarded as a fibre composite made of cellulose microfibrils embedded into a matrix of hemicelluloses reinforced with lignin [1]. Certain bones, or parts of bones, display at higher levels of hierarchy a spongy network of trabeculae, whose material itself might consist of porous hollow fibres; at lower levels of hierarchy, the cell wall is a composite of collagen and mineral nanoparticles made of carbonated hydroxyapatite [2, 3]. Nacre, the material of seashells, is made of an ordered multi-layered arrangement of mineral calcium carbonate tablets, embedded in a soft organic matrix. Although the constituents are structurally poor, their peculiar arrangement provides exceptional toughness properties [4]. In general, the superposition of multiple levels of structural hierarchy can impart multifunctional properties to the material. This effect has been proved to be remarkable. Ortiz [5] showed that the microstructure of several
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