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

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Author information

Affiliations

Authors

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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Keywords

  • Hashin Shtrikman
  • Material Geometry
  • Moderate Relative Density
  • Zener Anisotropy Ratio
  • Systems Materials Engineering

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