Size effect anomalies in the behaviour of loaded 3D mechanical metamaterials

Martin Dunn, Marcus Wheel

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
15 Downloads (Pure)


Size effects exhibited by mechanical metamaterials when loaded may be positive such that reducing overall size towards that of the length scale of the underlying structure intrinsic to the material is accompanied by increasing stiffness or rigidity, a phenomenon that has been repeatedly observed and is also forecast by various more generalised continuum theories of deformation in loaded heterogeneous continua. However, such effects may in certain circumstances be contradictory in that decreasing size is accompanied by increasing compliance, the transition from the conventional, positive to this theoretically unanticipated negative behaviour having been explained recently in terms of the distribution of material within 2D continua subject to bending. Here we report on a novel phenomenon newly observed in periodic 3D lattice materials comprised of repeated cubic unit cells formed of exterior edge and interior diagonal connectors. Subtle redistribution of matrix material from edges to diagonals causes the size effect to change dramatically, inverting from positive to negative when loaded in the torsional mode while the corresponding effect for the flexural mode remains entirely positive under the same circumstances. This observation may lead to the prospect of optimising the design of 3D periodic metamaterials to provide a stiffer response in one loading mode and a more compliant response in another, a feature that could potentially be exploited in various innovative applications.
Original languageEnglish
Pages (from-to)139-156
Number of pages18
JournalPhilosophical Magazine
Issue number2
Early online date28 Sep 2019
Publication statusPublished - 17 Jan 2020


  • mechanical metamaterial
  • size effect
  • Cosserat elasticity
  • additive manufacturing
  • 3D printing


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