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Impact of node geometry on the effective stiffness of non-slender three-dimensional truss lattice architectures

Portela, Carlos M. and Greer, Julia R. and Kochmann, Dennis M. (2018) Impact of node geometry on the effective stiffness of non-slender three-dimensional truss lattice architectures. Extreme Mechanics Letters, 22 . pp. 138-148. ISSN 2352-4316.

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Three-dimensional (3D), lattice-based micro- and nano-architected materials can possess desirable mechanical properties that are unattainable by homogeneous materials. Manufacturing these so-called structural metamaterials at the nano- and microscales typically results in non-slender architectures (e.g., struts with a high radius-to-length ratio r∕l), for which simple analytical and computational tools are inapplicable since they fail to capture the effects of nodes at strut junctions. We report a detailed analysis that quantifies the effect of nodes on the effective Young’s modulus (E∗) of lattice architectures with different unit cell geometries through (i) simple analytical constructions, (ii) reduced-order computational models, and (iii) experiments at the milli- and micrometer scales. The computational models of variable-node lattice architectures match the effective stiffness obtained from experiments and incur computational cost that are three orders-of-magnitude lower than alternative, conventional methods. We highlight a difference in the contribution of nodes to rigid versus non-rigid architectures and propose an extension to the classical stiffness scaling laws of the form E∗∝C_1(r∕l)α+C_2(r∕l)^β, which holds for slender and non-slender beam-based architectures, where constants C_1 and C_2 change with lattice geometry. We find the optimal scaling exponents for rigid architectures to be α=2 and β=4, and α=4 and β=6 for non-rigid architectures. These analytical, computational, and experimental results quantify the specific contribution of nodes to the effective stiffness of beam-based architectures and highlight the necessity of incorporating their effects into calculations of the structural stiffness. This work provides new, efficient tools that accurately capture the mechanics and physics of strut junctions in 3D, beam-based architected materials.

Item Type:Article
Related URLs:
URLURL TypeDescription
Portela, Carlos M.0000-0002-2649-4235
Greer, Julia R.0000-0002-9675-1508
Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2018 Elsevier Ltd. Received 5 April 2018, Revised 12 June 2018, Accepted 12 June 2018, Available online 19 June 2018.
Subject Keywords:Truss lattices; Reduced-order models; Architected materials; Cellular solids; Mechanics
Record Number:CaltechAUTHORS:20180620-151712137
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Official Citation:Carlos M. Portela, Julia R. Greer, Dennis M. Kochmann, Impact of node geometry on the effective stiffness of non-slender three-dimensional truss lattice architectures, Extreme Mechanics Letters, Volume 22, 2018, Pages 138-148, ISSN 2352-4316, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87274
Deposited By: Tony Diaz
Deposited On:20 Jun 2018 22:36
Last Modified:03 Oct 2019 19:54

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