Design and mechanical properties of elastically isotropic trusses
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The present article addresses design of stiff, elastically isotropic trusses and their mechanical properties. Isotropic trusses are created by combining two or more elementary cubic trusses in appropriate proportions and with their respective nodes lying on a common space lattice. Two isotropic binary compound trusses and many isotropic ternary trusses are identiﬁed, all with Young’s moduli equal to the maximal possible value for isotropic strut-based structures. In ﬁnitesized trusses, strain elevations are obtained in struts near the external free boundaries: a consequence of reduced nodal connectivity and thus reduced constraint on strut deformation and rotation. Although the boundary effects persist over distances of only about two unit cell lengths and have minimal effect on elastic properties, their manifestations in failure are more nuanced, especially when failure occurs by modes other than buckling (yielding or fracture). Exhaustive analyses are performed to glean insights into the mechanics of failure of such trusses.
Periodic truss structures can be designed to have high speciﬁc strength and speciﬁc stiffness in combination with other desirable attributes, including high energy absorption capacity1–3 and effective internal heat exchange.4,5 Most truss topologies, however, exhibit strongly anisotropic mechanical properties: an undesirable characteristic when trusses are used in applications in which the directions of loading are not known a priori. The present study addresses the design of lightweight (low relative density) truss structures that are elastically isotropic and that also exhibit high strength. The designs are based principally on compound trusses comprising two or more elementary cubic trusses that, on their own, are highly anisotropic. Realizing these and other designs has been made possible by recent advancements in additive manufacturing. For example, polymeric and polymer-derived ceramic trusses have been fabricated using self-propagating photopolymerization.6–8 Very low relative density metallic lattices have been formed by electroplating and etching away a polymeric template.9,10 Novel lithography techniques such as direct laser writing and projection micro-stereolithography have been used to fabricate fractal-like trusses composed of self-similar members that span length scales of several orders of magnitude.11,12 Experimental measurements and theoretical analyses have shown that these hierarchical structures exhibit nearly linear scaling of stiffness and strength even at very low relative densities (,1%).13–15 Contributing Editor: Lorenzo Valdevit a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2018.2
To achieve linear scaling between mechanical properties and relative density, truss deformation must be dominated by strut stretching. In stretch-dominated trusses, struts are loaded axially in either tension or compression, and thus, the macroscopic truss stiffness is proportional to the extensional strut stiffness. Since extensiona