Robust Design of Cellular Materials With Topological and Dimensional Imperfections

Abstract

A paradigm shift is underway in which the classical materials selection approach in engineering design is being replaced by the design of material structure and processing paths on a hierarchy of length scales for multifunctional performance requirements. In this paper, the focus is on designing mesoscopic material topology-the spatial arrangement of solid phases and voids on length scales larger than microstructures but smaller than the characteristic dimensions of an overall product. A robust topology design method is presented for designing materials on mesoscopic scales by topologically and parametrically tailoring them to achieve properties that are superior to those of standard or heuristic designs, customized for large-scale applications, and less sensitive to imperfections in the material. Imperfections are observed regularly in cellular material mesostructure and other classes of materials because of the stochastic influence of feasible processing paths. The robust topology design method allows us to consider these imperfections explicitly in a materials design process. As part of the method, guidelines are established for modeling dimensional and topological imperfections, such as tolerances and cracked cell walls, as deviations from intended material structure. Also, as part of the method, * Corresponding Author. Email: ccseepersad@mail.utexas.edu. Phone: (512) 471-1985. Fax: (512) Standard deviation of elastic constant values due to topological imperfections FRAME OF REFERENCEThe properties of materials are influenced by complex relationships with multi-scale material structure and associated processing paths. Process-structure-property relationships are often cast in terms of microstructural aspects of the material, including the arrangement of phases, grains, and defects such as vacancies, dislocations, or cracks, but it is also important to investigate other length scales. Larger mesostructural length scales, 1 for example, are characteristic of the prismatic cellular materials illustrated in Figure 1 and may take the form of cell dimensions, shape, and arrangement and cell wall dimensions and connectivity-features that strongly influence a wide range of desirable properties of these materials.[ INSERT FIGURE 1.] Typically, the properties of cellular materials are designed by selecting a cellular topology from a small set of standard topologies (e.g., square, triangular, hexagonal) and then adjusting its relative density by modifying the cell wall thickness. Topology changes have a strong impact on cellular material properties, but the small library of standard topologies limits our ability to reach some regions of a property space, as illustrated in Figure 2 for in-plane, effective elastic 1 Mesoscopic length scales (on the order of tens to hundreds of micrometers in this research) are intermediate between microscopic length scales, which apply to characteristics like gradients of chemical composition and microstructure (e.g., grain boundaries, dislocations, crystal structure), and m...

Lightweight Metal Cellular Structures Fabricated via 3D Printing of Sand Cast Molds

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Robust topology optimization accounting for spatially varying manufacturing errors

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Manufacturing tolerant topology optimization

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