Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T07:24:26.870Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical models of the geometric properties of solid and hollow architected lattice cellular materials

Published online by Cambridge University Press:  23 November 2017

Christopher J. Ro  and
Christopher S. Roper Open the ORCID record for Christopher S. Roper [Opens in a new window]
Christopher J. Ro*
Affiliation:
HRL Laboratories, LLC, Malibu, California 90265, USA
Christopher S. Roper*
Affiliation:
HRL Laboratories, LLC, Malibu, California 90265, USA
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

New closed-form analytical equations for volume fractions and surface-area-to-volume ratios for architected lattice cellular materials are derived. Prior approximate equations which erroneously over count overlapping volumes and the associated surface area are commonly used in the literature. These equations are found to have up to 184% error for volume fraction calculations for hollow lattices and 211% error for surface-area-to-volume ratio calculations, thus necessitating computational methods to arrive at accurate geometric properties for cellular lattice materials. This work derives new equations which are accurate to better than 1% for both volume fraction and surface-area-to-volume ratio as compared to the computational models. These new equations for cellular lattice materials are applicable to both pyramidal and tetrahedral unit cells as well as to both hollow and solid lattice members. By eliminating the need for numerical models to compute accurate volume fractions and surface-area-to-volume ratios of architected cellular materials, these new analytical equations will enable accurate yet computationally efficient optimization of the physical properties of architected cellular materials.

Keywords

cellular (material form)porosity
Type
Invited Articles
Information
Journal of Materials Research , Volume 33 , Issue 3: Focus Issue: Architected Materials , 14 February 2018 , pp. 264 - 273
Check for updates
Copyright
Copyright © Materials Research Society 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Contributing Editor: Lorenzo Valdevit

References

REFERENCES

Evans, A.G., Hutchinson, J.W., Fleck, N.A., Ashby, M.F., and Wadley, H.N.G.: The topological design of multifunctional cellular metals. Prog. Mater. Sci. 46, 309 (2001).Google Scholar
Chiras, S., Mumm, D.R., Evans, A.G., Wicks, N., Hutchinson, J.W., Dharmasena, K., Wadley, H.N.G., and Fichter, S.: The structural performance of near-optimized truss core panels. Int. J. Solids Struct. 39, 4093 (2002).Google Scholar
Wicks, N. and Hutchinson, J.W.: Performance of sandwich plates with truss cores. Mech. Mater. 36, 739 (2004).Google Scholar
Schaedler, T.A., Ro, C.J., Sorensen, A.E., Eckel, Z., Yang, S.S., Carter, W.B., and Jacobsen, A.J.: Designing metallic microlattices for energy absorber applications. Adv. Eng. Mater. 16, 276 (2014).Google Scholar
Evans, A.G., He, M.Y., 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).Google Scholar
Lu, T.J., Stone, H.A., and Ashby, M.F.: Heat transfer in open-cell metal foams. Acta Mater. 46, 3619 (1998).CrossRefGoogle Scholar
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).Google Scholar
Roper, C.S., Schubert, R.C., Maloney, K.J., Page, D., Ro, C.J., Yang, S.S., and Jacobsen, A.J.: Scalable 3D bicontinuous fluid networks: Polymer heat exchangers toward artificial organs. Adv. Mater. 27, 2479–2484 (2015).Google Scholar
Jones, J.R., Lin, S., Yue, S., Lee, P.D., Hanna, J.V., Smith, M.E., and Newport, R.J.: Bioactive glass scaffolds for bone regeneration and their hierarchical characterisation. Proc. Inst. Mech. Eng., Part H 224, 1373 (2010).CrossRefGoogle ScholarPubMed
Lu, T.J., Hess, A., and Ashby, M.F.: Sound absorption in metallic foams. J. Appl. Phys. 85, 7528 (1999).Google Scholar
Ashby, M.F.: The properties of foams and lattices. Philos. Trans. R. Soc., A 364, 15 (2006).Google Scholar
Wadley, H.N.G.: Cellular metals manufacturing. Adv. Eng. Mater. 4, 726 (2002).Google Scholar
Finnegan, K., Kooistra, G., Wadley, H.N.G., and Deshpande, V.S.: The compressive response of carbon fiber composite pyramidal truss sandwich cores. Int. J. Mater. Res. 98, 1264 (2007).Google Scholar
Gibson, L.J. and Ashby, M.F.: The mechanics of three-dimensional cellular materials. Philos. Trans. R. Soc., A 382, 43 (1982).Google Scholar
Gibson, L. and Ashby, M.F.: Cellular Solids: Structure and Properties, 2nd ed. (Cambridge University Press, Cambridge, U.K., 1997).Google Scholar
Gibson, L.J., Ashby, M.F., and Harley, B.A.: Cellular Materials in Nature and Medicine (Cambridge University Press, Cambridge, U.K., 2010).Google Scholar
Deshpande, V.S., Ashby, M.F., and Fleck, N.A.: Foam topology: Bending versus stretching dominated architectures. Acta Mater. 49, 1035 (2001).Google Scholar
Jacobsen, A.J., Barvosa-Carter, W., and Nutt, S.: Compression behavior of micro-scale truss structures formed from self-propagating polymer waveguides. Acta Mater. 55, 6724 (2007).Google 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).Google Scholar
Lu, T., Valdevit, L., and Evans, A.: Active cooling by metallic sandwich structures with periodic cores. Prog. Mater. Sci. 50, 789 (2005).Google Scholar
Wadley, H.N.G., Fleck, N.A., and Evans, A.G.: Fabrication and structural performance of periodic cellular metal sandwich structures. Compos. Sci. Technol. 63, 2331 (2003).CrossRefGoogle Scholar
Queheillalt, D.T. and Wadley, H.N.G.: Pyramidal lattice truss structures with hollow trusses. Mater. Sci. Eng., A 397, 132 (2005).CrossRefGoogle Scholar
Kooistra, G.W., Deshpande, V.S., and Wadley, H.N.G.: Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminium. Acta Mater. 52, 4229 (2004).Google Scholar
Wang, J., Evans, A.G., Dharmasena, K., and Wadley, H.N.G.: On the performance of truss panels with Kagomé cores. Int. J. Solids Struct. 40, 6981 (2003).Google 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).Google Scholar
Maloney, K.J., Roper, C.S., Jacobsen, A.J., Carter, W.B., Valdevit, L., and Schaedler, T.A.: Microlattices as architected thin films: Analysis of mechanical properties and high strain elastic recovery. APL Mater. 1, 022106 (2013).CrossRefGoogle Scholar
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).Google 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
Fink, K.D., Kolodziejska, J.A., Jacobsen, A.J., and Roper, C.S.: Fluid dynamics of flow through microscale lattice structures formed from self-propagating photopolymer waveguides. AIChE J. 57, 2636 (2011).CrossRefGoogle Scholar
Roper, C.S., Fink, K.D., Lee, S.T., Kolodziejska, J.A., and Jacobsen, A.J.: Anisotropic convective heat transfer in microlattice materials. AIChE J. 59, 622 (2013).Google Scholar
Wicks, N. and Hutchinson, J.W.: Optimal truss plates. Int. J. Solids Struct. 38, 5165 (2001).CrossRefGoogle Scholar
Valdevit, L., Jacobsen, A.J., Greer, J.R., and Carter, W.B.: Protocols for the optimal design of multi-functional cellular structures: From hypersonics to micro-architected materials. J. Am. Ceram. Soc. 94, s15 (2011).Google Scholar
Jacobsen, A.J., Barvosa-Carter, W., and Nutt, S.: Shear behavior of polymer micro-scale truss structures formed from self-propagating polymer waveguides. Acta Mater. 56, 1209 (2008).CrossRefGoogle Scholar
Wadley, H.N.G.: Multifunctional periodic cellular metals. Philos. Trans. R. Soc., A 364, 31 (2006).Google 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).Google Scholar
Deshpande, V.S. and Fleck, N.A.: Collapse of truss core sandwich beams in 3-point bending. Int. J. Solids Struct. 38, 6275 (2001).Google Scholar
Valdevit, L., Godfrey, S.W., Schaedler, T.A., Jacobsen, A.J., and Carter, W.B.: Compressive strength of hollow microlattices: Experimental characterization, modeling, and optimal design. J. Mater. Res. 28, 2461 (2013).Google Scholar
Hammetter, C.I., Rinaldi, R.G., and Zok, F.W.: Pyramidal lattice structures for high strength and energy absorption. J. Appl. Mech. 80, 041014-1–041014-11 (2013).CrossRefGoogle Scholar
Roper, C.S.: Multiobjective optimization for design of multifunctional sandwich panel heat pipes with micro-architected truss cores. Int. J. Heat Fluid Flow 32, 239 (2011).CrossRefGoogle Scholar
Moreton, M.: Symmetrical intersections of right circular cylinders. Math. Gaz. 58, 181 (1974).Google Scholar
Angell, I.O. and Moore, M.: Symmetrical intersections of cylinders. Acta Crystallogr., Sect. A: Found. Crystallogr. 43, 244 (1987).Google Scholar
Jacobsen, A.J., Kolodziejska, J.A., Doty, R., Fink, K.D., Zhou, C., Roper, C.S., and Carter, W.B.: Interconnected self-propagating photopolymer waveguides: An alternative to stereolithography for rapid formation of lattice-based open-cellular materials. In 21st Annual International Solid Freeform Fabrication Symposium—An Additive Manufacturing Conference, SFF 2010 (2010); p. 846.Google Scholar