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Berger et al. reply

Nature volume 564, pages E2–E4 (2018)Cite this article

replying to G. W. Milton, Nature 564, https://doi.org/10.1038/s41586-018-0724-8 (2018)

In the accompanying Comment1, Milton correctly points out that material geometries that achieve the Hashin–Shtrikman upper bounds2 have been previously identified. We thank G. W. Milton for his interest in our work3 and welcome his insights, including those that look beyond our contribution in regard to elasticities that are realizable.

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Fig. 1: Young’s, shear and bulk moduli.
Fig. 2: Total stiffness.

References

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Author information

Authors and Affiliations

  1. Materials Department, University of California, Santa Barbara, CA, USA

    J. B. Berger & R. M. McMeeking

  2. Department of Mechanical Engineering, University of California, Santa Barbara, CA, USA

    J. B. Berger & R. M. McMeeking

  3. Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Virginia, Charlottesville, VA, USA

    H. N. G. Wadley

  4. School of Engineering, University of Aberdeen, King’s College, Aberdeen, UK

    R. M. McMeeking

  5. INM-Leibniz Institute for New Materials, Saarbrücken, Germany

    R. M. McMeeking

Authors
  1. J. B. Berger
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  2. H. N. G. Wadley
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  3. R. M. McMeeking
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Contributions

J.B.B. created the ideas, conceived and designed the new material geometries and performed the structural analysis. R.M.M. developed the analytical models for the strain energy and moduli and, with H.N.G.W., contributed to refining the concepts, contextualizing the results and providing critiques and assessments.

Corresponding author

Correspondence to J. B. Berger.

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Competing interests

The material geometry identified in this work to achieve the theoretical bounds in performance has been included in a Patent Cooperation Treaty (PCT/US2015/010458) by Nama Development, LLC (DE), which is majority-owned by J.B.B.

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Berger, J.B., Wadley, H.N.G. & McMeeking, R.M. Berger et al. reply. Nature 564, E2–E4 (2018). https://doi.org/10.1038/s41586-018-0725-7

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