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Title: Optimal lattice-structured materials

Abstract

This paper describes a method for optimizing the mesostructure of lattice-structured materials. These materials are periodic arrays of slender members resembling efficient, lightweight macroscale structures like bridges and frame buildings. Current additive manufacturing technologies can assemble lattice structures with length scales ranging from nanometers to millimeters. Previous work demonstrates that lattice materials have excellent stiffness- and strength-to-weight scaling, outperforming natural materials. However, there are currently no methods for producing optimal mesostructures that consider the full space of possible 3D lattice topologies. The inverse homogenization approach for optimizing the periodic structure of lattice materials requires a parameterized, homogenized material model describing the response of an arbitrary structure. This work develops such a model, starting with a method for describing the long-wavelength, macroscale deformation of an arbitrary lattice. The work combines the homogenized model with a parameterized description of the total design space to generate a parameterized model. Finally, the work describes an optimization method capable of producing optimal mesostructures. Several examples demonstrate the optimization method. One of these examples produces an elastically isotropic, maximally stiff structure, here called the isotruss, that arguably outperforms the anisotropic octet truss topology.

Authors:
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1305867
Alternate Identifier(s):
OSTI ID: 1397718
Report Number(s):
LLNL-JRNL-683819
Journal ID: ISSN 0022-5096
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of the Mechanics and Physics of Solids
Additional Journal Information:
Journal Volume: 96; Journal Issue: C; Journal ID: ISSN 0022-5096
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 42 ENGINEERING; lattice materials; microstructures; optimization

Citation Formats

Messner, Mark C. Optimal lattice-structured materials. United States: N. p., 2016. Web. doi:10.1016/j.jmps.2016.07.010.
Messner, Mark C. Optimal lattice-structured materials. United States. doi:10.1016/j.jmps.2016.07.010.
Messner, Mark C. Sat . "Optimal lattice-structured materials". United States. doi:10.1016/j.jmps.2016.07.010. https://www.osti.gov/servlets/purl/1305867.
@article{osti_1305867,
title = {Optimal lattice-structured materials},
author = {Messner, Mark C.},
abstractNote = {This paper describes a method for optimizing the mesostructure of lattice-structured materials. These materials are periodic arrays of slender members resembling efficient, lightweight macroscale structures like bridges and frame buildings. Current additive manufacturing technologies can assemble lattice structures with length scales ranging from nanometers to millimeters. Previous work demonstrates that lattice materials have excellent stiffness- and strength-to-weight scaling, outperforming natural materials. However, there are currently no methods for producing optimal mesostructures that consider the full space of possible 3D lattice topologies. The inverse homogenization approach for optimizing the periodic structure of lattice materials requires a parameterized, homogenized material model describing the response of an arbitrary structure. This work develops such a model, starting with a method for describing the long-wavelength, macroscale deformation of an arbitrary lattice. The work combines the homogenized model with a parameterized description of the total design space to generate a parameterized model. Finally, the work describes an optimization method capable of producing optimal mesostructures. Several examples demonstrate the optimization method. One of these examples produces an elastically isotropic, maximally stiff structure, here called the isotruss, that arguably outperforms the anisotropic octet truss topology.},
doi = {10.1016/j.jmps.2016.07.010},
journal = {Journal of the Mechanics and Physics of Solids},
number = C,
volume = 96,
place = {United States},
year = {Sat Jul 09 00:00:00 EDT 2016},
month = {Sat Jul 09 00:00:00 EDT 2016}
}

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Cited by: 3 works
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