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. 2018 Jun 14;8:9139. doi: 10.1038/s41598-018-26980-7

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Tunable actuation strain and modulus in programmable multi-material metamaterials (A) Tunable transverse actuation strain tuning as a function of longitudinal strain. The negative expansion in transverse direction can be modulated through combinations of dissimilar Young’s modulus in (r) and (v) strut members within a single auxetic 3D honeycomb microlattice. (B) Plot of Poisson’s ratio vs. Young’s modulus/Shear modulus of architected metamaterials in comparison with bulk materials. R refers to Young’s modulus gradient within the micro-architecture of the metamaterials.