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A Fully-Nonlocal Quasicontinuum Method to Model the Nonlinear Response of Periodic Truss Lattices


Phlipot, Gregory Paul (2019) A Fully-Nonlocal Quasicontinuum Method to Model the Nonlinear Response of Periodic Truss Lattices. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3MPP-Q119.


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 a polynomial 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 compare coarse-grained simulations to fully-resolved simulations for various test problems, including: brittle fracture toughness prediction, static and dynamic indentation with geometric and material nonlinearities, and uniaxial tension of a truss lattice plate with a cylindrical hole. We also discover the notion of stretch locking --- a phenomenon where certain lattice topologies are over-constrained, resulting in artificially stiff behavior similar to volumetric locking in finite elements --- and show that using higher-order interpolation instead of affine interpolation significantly reduces the error in the presence of stretch locking in 2D and 3D. Overall, the new technique shows convincing agreement with exact, discrete results for a wide variety of 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:Thesis (Dissertation (Ph.D.))
Subject Keywords:Quasicontinuum, Truss Lattice, Multilattice, Locking
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Space Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kochmann, Dennis M.
Thesis Committee:
  • Daraio, Chiara (chair)
  • Ortiz, Michael
  • Asimaki, Domniki
  • Kochmann, Dennis M.
Defense Date:16 May 2019
Non-Caltech Author Email:gpphlipot (AT)
Funding AgencyGrant Number
NASA Space Technology Research FellowshipNNX16AM58H
Office of Naval ResearchN00014-16-1-2431
Record Number:CaltechTHESIS:05242019-115317802
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for chapters 3 and 4
Phlipot, Gregory Paul0000-0003-2721-8678
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11541
Deposited By: Gregory Phlipot
Deposited On:04 Jun 2019 22:05
Last Modified:28 Oct 2021 22:47

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