On three-dimensional dilational elastic metamaterials

By Tiemo Bückmann, R. Schittny, Michael Thiel, Muamer Kadic, Graeme W. Milton, M. Wegener. 2013

183 citations recorded by the source corpus.

Dilational materials are stable, three-dimensional isotropic auxetics with an ultimate Poisson's ratio of −1. Inspired by previous theoretical work, we design a feasible blueprint for an artificial material, a metamaterial, which approaches the ideal of a dilational material. The main novelty of our work is that we also fabricate and characterize corresponding metamaterial samples. To reveal all modes in the design, we calculate the phonon band structures. On this basis, using cubic symmetry we can unambiguously retrieve all different non-zero elements of the rank-four effective metamaterial elasticity tensor from which all effective elastic metamaterial properties follow. While the elastic properties and the phase velocity remain anisotropic, the effective Poisson's ratio indeed becomes isotropic and approaches −1 in the limit of small internal connections. This finding is also supported by independent, static continuum-mechanics calculations. In static experiments on macroscopic polymer structures fabricated by three-dimensional printing, we measure Poisson's ratios as low as −0.8 in good agreement with the theory. Microscopic samples are also presented.

Subfields: Biomedical Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/d5c2acd4acb60fa684665fd089cf93a4523e7356

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. J. Markmann
2. Celal Soyarslan
3. Wei Peng
4. C. Ha
5. Swantje Bargmann
6. R. Lakes
7. M. Plesha

In Mechanical Engineering

1. R. Lakes
2. C. Ha
3. M. Plesha
4. Wei Peng
5. Wenwang Wu
6. Xiang Li
7. Yang Lu
8. Jian Xiong

Citations in the corpus

• Auxetic mechanical metamaterials: from soft to stiff (2023, methodology): “Reprinted from [119], Copyright (2020), with permission from Elsevier); (e) 2D chiral and anti-chiral structures (Reprinted from [127], Copyright (2010), with permission from Elsevier); and (f) 3D chiral and anti-chiral structures (Reproduced from [128].”
• Chiral three‐dimensional isotropic lattices with negative Poisson's ratio (2016, methodology): “3D lattices with a negative Poisson’s ratio [21] have been designed and fabricated.”
• Additive manufacturing of metallic components by selective electron beam melting — a review (2016, background): “Certain cell architectures develop full phononic band gaps where the propagation of elastic waves within a broad frequency band is completely suppressed.(93,101) Generally, cellular materials consisting of these rather complex unit cells are difficult to realise with conventional methods.”
• Design for Additive Manufacturing (2019, methodology): “For example, AM has been used to produce ultra light and stiff structures [374], auxetic structures [51][143][282] and the molds for the unit cells for auxetic structures [32], and could be used to produce the chiral honeycomb auxetic structures proposed by [177].”
• Generation of 3D representative volume elements for heterogeneous materials: A review (2018, background): “Figures reprinted from [519], under the terms of the Creative Commons Attribution 3.”
• Chiral three-dimensional lattices with tunable Poisson’s ratio (2016, methodology): “Also, 3D lattices have been made with a negative Poisson’s ratio [17].”