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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: csroper@hrl.com
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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
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Copyright
Copyright © Materials Research Society 2017 

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Footnotes

Contributing Editor: Lorenzo Valdevit

References

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