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A quasicontinuum theory for the nonlinear mechanical response of general periodic truss lattices

Phlipot, Gregory P. and Kochmann, Dennis M. (2019) A quasicontinuum theory for the nonlinear mechanical response of general periodic truss lattices. Journal of the Mechanics and Physics of Solids, 124 . pp. 758-780. ISSN 0022-5096.

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We present a framework for the efficient, yet accurate description of general periodic truss networks based on concepts of the quasicontinuum (QC) method. Previous research in coarse-grained truss models has focused either on simple bar trusses or on two-dimensional beam lattices undergoing small deformations. Here, we extend the truss QC methodology to nonlinear deformations, general periodic beam lattices, and three dimensions. We introduce geometric nonlinearity into the model by using a corotational beam description at the level of individual truss members. Coarse-graining is achieved by the introduction of representative unit cells and an affine interpolation analogous to traditional QC. General periodic lattices defined by the periodic assembly of a single unit cell are modeled by retaining all unique degrees of freedom of the unit cell (identified by a lattice decomposition into simple Bravais lattices) at each macroscopic point in the simulation, and interpolating each degree of freedom individually. We show that this interpolation scheme accurately captures the homogenized properties of periodic truss lattices for uniform deformations. In order to showcase the efficiency and accuracy of the method, we perform simulations to predict the brittle fracture toughness of multiple lattice architectures and compare them to results obtained from significantly more expensive discrete truss simulations. Finally, we demonstrate the applicability of the method for nonlinear elastic truss lattices undergoing finite deformations. Overall, the new technique shows convincing agreement with exact, discrete results for most lattice architectures, and offers opportunities to reduce computational expenses in structural lattice simulations and thus to efficiently extract the effective mechanical performance of discrete networks.

Item Type:Article
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Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2018 Elsevier Ltd. Received 18 May 2018, Revised 16 October 2018, Accepted 23 November 2018, Available online 26 November 2018. The authors gratefully acknowledge the support from the Office of Naval Research through award N00014-16-1-2431. This work was supported by a NASA Space Technology Research Fellowship.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-16-1-2431
NASA Space Technology Research FellowshipNNX16AM58H
Subject Keywords:Truss lattice; Multiscale modeling; Homogenization; Finite elements; Fracture
Record Number:CaltechAUTHORS:20181126-102125266
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Official Citation:Gregory P. Phlipot, Dennis M. Kochmann, A quasicontinuum theory for the nonlinear mechanical response of general periodic truss lattices, Journal of the Mechanics and Physics of Solids, Volume 124, 2019, Pages 758-780, ISSN 0022-5096, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91161
Deposited By: Tony Diaz
Deposited On:26 Nov 2018 18:37
Last Modified:03 Oct 2019 20:32

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