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Design and mechanical properties of elastically isotropic trusses

Published online by Cambridge University Press:  14 February 2018

Ryan M. Latture Open the ORCID record for Ryan M. Latture [Opens in a new window] ,
Matthew R. Begley  and
Frank W. Zok
Ryan M. Latture
Affiliation:
Materials Department, University of California, Santa Barbara, California 93106, USA
Matthew R. Begley
Affiliation:
Materials Department, University of California, Santa Barbara, California 93106, USA
Frank W. Zok*
Affiliation:
Materials Department, University of California, Santa Barbara, California 93106, USA
*
a)Address all correspondence to this author. e-mail: zok@ucsb.edu
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Abstract

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 finite-sized 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.

Keywords

cellular (material type)elastic propertiesstrength
Type
Invited Articles
Information
Journal of Materials Research , Volume 33 , Issue 3: Focus Issue: Architected Materials , 14 February 2018 , pp. 249 - 263
Copyright
Copyright © Materials Research Society 2018 

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Footnotes

Contributing Editor: Lorenzo Valdevit

References

REFERENCES

Zheng, J., Zhao, L., and Fan, H.: Energy absorption mechanisms of hierarchical woven lattice composites. Composites, Part B 43, 1516 (2012).CrossRefGoogle Scholar
Evans, A.G., He, M., Deshpande, V.S., Hutchinson, J.W., Jacobsen, A.J., and Carter, W.B.: Concepts for enhanced energy absorption using hollow micro-lattices. Int. J. Impact Eng. 37, 947 (2010).CrossRefGoogle Scholar
Asadpoure, A., Tootkaboni, M., and Valdevit, L.: Topology optimization of multiphase architected materials for energy dissipation. Comput. Methods Appl. Mech. Eng. 325, 314–329 (2017).CrossRefGoogle Scholar
Wadley, H.N.G.: Multifunctional periodic cellular metals. Philos. Trans. R. Soc. London, Ser. A 364, 31 (2006).Google ScholarPubMed
Maloney, K.J., Fink, K.D., Schaedler, T.A., Kolodziejska, J.A., Jacobsen, A.J., and Roper, C.S.: Multifunctional heat exchangers derived from three-dimensional micro-lattice structures. Int. J. Heat Mass Transfer 55, 2486 (2012).CrossRefGoogle Scholar
Jacobsen, A.J., Barvosa-Carter, W., and Nutt, S.: Micro-scale truss structures formed from self-propagating photopolymer waveguides. Adv. Mater. 19, 3892 (2007).CrossRefGoogle Scholar
Jacobsen, A.J., Barvosa-Carter, W., and Nutt, S.: Micro-scale truss structures with three-fold and six-fold symmetry formed from self-propagating polymer waveguides. Acta Mater. 56, 2540 (2008).CrossRefGoogle Scholar
Eckel, Z.C., Zhou, C., Martin, J.H., Jacobsen, A.J., Carter, W.B., and Schaedler, T.A.: Additive manufacturing of polymer-derived ceramics. Science 351, 3 (2016).CrossRefGoogle ScholarPubMed
Schaedler, T.A., Jacobsen, A.J., Torrents, A., Sorensen, A.E., Lian, J., Greer, J.R., Valdevit, L., and Carter, W.B.: Ultralight metallic microlattices. Science 334, 962 (2011).CrossRefGoogle ScholarPubMed
Torrents, A., Schaedler, T.A., Jacobsen, A.J., Carter, W.B., and Valdevit, L.: Characterization of nickel-based microlattice materials with structural hierarchy from the nanometer to the millimeter scale. Acta Mater. 60, 3511 (2012).CrossRefGoogle Scholar
Meza, L.R., Zelhofer, A.J., Clarke, N., Mateos, A.J., Kochmann, D.M., and Greer, J.R.: Resilient 3D hierarchical architected metamaterials. Proc. Natl. Acad. Sci. U. S. A. 112, 11502 (2015).CrossRefGoogle ScholarPubMed
Zheng, X., Smith, W., Jackson, J., Moran, B., Cui, H., Chen, D., Ye, J., Fang, N., Rodriguez, N., Weisgraber, T., and Spadaccini, C.M.: Multiscale metallic metamaterials. Nat. Mater. 15, 1100 (2016).CrossRefGoogle ScholarPubMed
Lakes, R.: Materials with structural hierarchy. Nature 361, 511 (1993).CrossRefGoogle Scholar
Zheng, X., Lee, H., Weisgraber, T.H., Shusteff, M., DeOtte, J., Duoss, E.B., Kuntz, J.D., Biener, M.M., Ge, Q., Jackson, J.A., Kucheyev, S.O., Fang, N.X., and Spadaccini, C.M.: Ultralight, ultrastiff mechanical metamaterials. Science 344, 1373 (2014).CrossRefGoogle ScholarPubMed
Jang, D., Meza, L.R., Greer, F., and Greer, J.R.: Fabrication and deformation of three-dimensional hollow ceramic nanostructures. Nat. Mater. 12, 893 (2013).CrossRefGoogle ScholarPubMed
Gibson, L.J. and Ashby, M.F.: Cellular Solids: Structure and Properties (Cambridge University Press, Cambridge, U.K., 1999).Google Scholar
Asadpoure, A. and Valdevit, L.: Topology optimization of lightweight periodic lattices under simultaneous compressive and shear stiffness constraints. Int. J. Solids Struct. 60, 1 (2015).CrossRefGoogle Scholar
Guth, D.C., Luersen, M.A., and Muñoz-Rojas, P.A.: Optimization of three-dimensional truss-like periodic materials considering isotropy constraints. Struct. Multidiscip. Optim. 52, 1 (2015).CrossRefGoogle Scholar
Buhl, T., Pedersen, C.B.W., and Sigmund, O.: Stiffness design of geometrically nonlinear structures using topology optimization. Struct. Multidiscip. Optim. 19, 93 (2000).CrossRefGoogle Scholar
Sigmund, O.: Tailoring materials with prescribed elastic properties. Mech. Mater. 20, 351 (1995).CrossRefGoogle Scholar
Osanov, M. and Guest, J.K.: Topology optimization for architected materials design. Annu. Rev. Mater. Res. 46, 211 (2016).CrossRefGoogle Scholar
Challis, V.J., Roberts, A.P., and Wilkins, A.H.: Design of three dimensional isotropic microstructures for maximized stiffness and conductivity. Int. J. Solids Struct. 45, 4130 (2008).CrossRefGoogle Scholar
Zok, F.W., Latture, R.M., and Begley, M.R.: Periodic truss structures. J. Mech. Phys. Solids 96, 184 (2016).CrossRefGoogle Scholar
Deshpande, V.S., Fleck, N.A., and Ashby, M.F.: Effective properties of the octet-truss lattice material. J. Mech. Phys. Solids 49, 1747 (2001).CrossRefGoogle Scholar
Gurtner, G. and Durand, M.: Stiffest elastic networks. Proc. R. Soc. London, Ser. A 470, 20130611 (2014).Google Scholar
Pettermann, H.E. and Hüsing, J.: Modeling and simulation of relaxation in viscoelastic open cell materials and structures. Int. J. Solids Struct. 49, 2848 (2012).CrossRefGoogle Scholar
Buxton, G.A. and Clarke, N.: Bending to stretching transition in disordered networks. Phys. Rev. Lett. 98, 1 (2007).CrossRefGoogle ScholarPubMed
Nye, J.F.: Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University Press, Oxford, U.K., 1985).Google Scholar
Wallach, J.C. and Gibson, L.J.: Mechanical behavior of a three-dimensional truss material. Int. J. Solids Struct. 38, 7181 (2001).CrossRefGoogle Scholar
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