Optimal latticestructured materials
Abstract
This paper describes a method for optimizing the mesostructure of latticestructured 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 strengthtoweight 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 longwavelength, 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:
 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
 Report Number(s):
 LLNLJRNL683819
Journal ID: ISSN 00225096
 Grant/Contract Number:
 AC5207NA27344
 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 00225096
 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 latticestructured materials. United States: N. p., 2016.
Web. doi:10.1016/j.jmps.2016.07.010.
Messner, Mark C. Optimal latticestructured materials. United States. doi:10.1016/j.jmps.2016.07.010.
Messner, Mark C. 2016.
"Optimal latticestructured materials". United States.
doi:10.1016/j.jmps.2016.07.010. https://www.osti.gov/servlets/purl/1305867.
@article{osti_1305867,
title = {Optimal latticestructured materials},
author = {Messner, Mark C.},
abstractNote = {This paper describes a method for optimizing the mesostructure of latticestructured 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 strengthtoweight 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 longwavelength, 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 = 2016,
month = 7
}

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