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Compressive stiffness of staggered woodpile lattices: mechanics, measurement, and scaling laws

Compressive stiffness of staggered woodpile lattices: mechanics, measurement, and scaling laws
Compressive stiffness of staggered woodpile lattices: mechanics, measurement, and scaling laws
Lattices in woodpile arrangement are of interest in many applications such as tissue engineering scaffolds, elastic metamaterials and lightweight structures: the choice in lattice arrangement and stacking parameters facilitate innovative material design. Additive manufacturing has enabled fabrication of such structured materials with tunable properties. Here, the elastic response of woodpile lattices is studied analytically, numerically, and experimentally when they are compressed in the stacking direction, with struts staggered in alternating layers. Expressions for the apparent Young’s modulus, and its dependence on porosity, are derived from the analysis of a periodically-supported, periodically-loaded, elastic filament. A fifth power law relating the apparent Young’s modulus with the volume fraction is obtained in the asymptotic limit of high porosity, which is consistent with scaling arguments presented here. When the stacking is asymmetric, the apparent stiffness is presented in terms of an analytically known function of the skewness parameter α. For dense lattices, departure from the proposed power law is observed in computational simulations, as well as laboratory experiments on polylactic acid (PLA) 3D-printed woodpiles. Variations from power law can be attributed to unaccounted for effects in the micromechanics of the filaments, e.g. filament shear and diametrical compression. The experimentally obtained relationship, between the apparent modulus and porosity, is in excellent agreement with our analysis and numerical results.
3D-Printing, Apparent elastic modulus, Lattice material, Woodpile structure
0020-7403
Cuan Urquizo, Enrique
0ba097ed-0d24-4c0b-896c-72e2f5c5cd59
Shalchy, Faezeh
b5c031f1-ccd4-4a41-b592-faeb0c8b9c69
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Cuan Urquizo, Enrique
0ba097ed-0d24-4c0b-896c-72e2f5c5cd59
Shalchy, Faezeh
b5c031f1-ccd4-4a41-b592-faeb0c8b9c69
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e

Cuan Urquizo, Enrique, Shalchy, Faezeh and Bhaskar, Atul (2020) Compressive stiffness of staggered woodpile lattices: mechanics, measurement, and scaling laws. International Journal of Mechanical Sciences, 187, [105932]. (doi:10.1016/j.ijmecsci.2020.105932).

Record type: Article

Abstract

Lattices in woodpile arrangement are of interest in many applications such as tissue engineering scaffolds, elastic metamaterials and lightweight structures: the choice in lattice arrangement and stacking parameters facilitate innovative material design. Additive manufacturing has enabled fabrication of such structured materials with tunable properties. Here, the elastic response of woodpile lattices is studied analytically, numerically, and experimentally when they are compressed in the stacking direction, with struts staggered in alternating layers. Expressions for the apparent Young’s modulus, and its dependence on porosity, are derived from the analysis of a periodically-supported, periodically-loaded, elastic filament. A fifth power law relating the apparent Young’s modulus with the volume fraction is obtained in the asymptotic limit of high porosity, which is consistent with scaling arguments presented here. When the stacking is asymmetric, the apparent stiffness is presented in terms of an analytically known function of the skewness parameter α. For dense lattices, departure from the proposed power law is observed in computational simulations, as well as laboratory experiments on polylactic acid (PLA) 3D-printed woodpiles. Variations from power law can be attributed to unaccounted for effects in the micromechanics of the filaments, e.g. filament shear and diametrical compression. The experimentally obtained relationship, between the apparent modulus and porosity, is in excellent agreement with our analysis and numerical results.

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Compressive stiffness of staggered woodpile lattices - Accepted Manuscript
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More information

Accepted/In Press date: 8 July 2020
e-pub ahead of print date: 9 July 2020
Published date: 1 December 2020
Keywords: 3D-Printing, Apparent elastic modulus, Lattice material, Woodpile structure

Identifiers

Local EPrints ID: 442336
URI: http://eprints.soton.ac.uk/id/eprint/442336
ISSN: 0020-7403
PURE UUID: 47b14dd9-0d2a-468f-822d-e09b6c8e617d

Catalogue record

Date deposited: 13 Jul 2020 16:39
Last modified: 25 Nov 2021 23:04

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Contributors

Author: Enrique Cuan Urquizo
Author: Faezeh Shalchy
Author: Atul Bhaskar

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