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Simple, accurate surrogate models of the elastic response of three-dimensional open truss micro-architectures with applications to multiscale topology design

  • Seth WattsEmail author
  • William Arrighi
  • Jun Kudo
  • Daniel A. Tortorelli
  • Daniel A. White
Research Paper

Abstract

Elastic meta-materials are those whose unique properties come from their micro-architecture, rather than, e.g., from their chemistry. The introduction of such architecture, which is increasingly able to be fabricated due to advances in additive manufacturing, expands the design domain and enables improved design, from the most complex multi-physics design problems to the simple compliance design problem that is our focus. Unfortunately, concurrent design of both the micro-scale and the macroscale is computationally very expensive when the former can vary spatially, particularly in three dimensions. Instead, we provide simple, accurate surrogate models of the homogenized linear elastic response of the isotruss, the octet truss, and the ORC truss based on high-fidelity continuum finite element analyses. These surrogate models are relatively accurate over the full range of relative densities, in contrast to analytical models in the literature, which we show lose accuracy as relative density increases. The surrogate models are also simple to implement, which we demonstrate by modifying Sigmund’s 99-line code to solve a three-dimensional, multiscale compliance design problem with spatially varying relative density. We use this code to generate examples in both two and three dimensions that illustrate the advantage of elastic meta-materials over structures with a single length scale, i.e., those without micro-architectures.

Keywords

Topology design Elasticity Finite element methods Surrogate model Multiscale 

Notes

Acknowledgments

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Funding information

This work received funding from LDRD number 17-SI-005. LLNL-JRNL-758077.

Compliance with ethical standards

Conflict of interests

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Computational Engineering DivisionLawrence Livermore National LaboratoryLivermoreUSA
  2. 2.Applications, Simulations, and Quality DivisionLawrence Livermore National LaboratoryLivermoreUSA
  3. 3.Center for Design and OptimizationLawrence Livermore National LaboratoryLivermoreUSA
  4. 4.Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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