Mechanical metamaterials are structures designed to exhibit an exotic response, such as topological soft modes at a surface. Here we explore single-material 3D prints of these topological structures by translating a ball-and-spring model into a physical prototype. By uniaxially compressing the 3D-printed solid having marginal rigidity, we observe that the surfaces are consistently softer than the bulk. However, we also find that either of two opposite surfaces can be the softest, in contrast to the topologically robust predictions of the linear model. Finite-element simulations allow us to bridge this gap. We explore how the printing geometry and deformation amplitude could affect surface softness. For small strains, we find qualitative agreement with the ball-and-spring model but, surprisingly, nonlinear deformations can select which side is softest. Our work contextualizes the predictions of topological mechanics for real 3D materials and their potential for cushioning applications.

Original languageEnglish
Article number101911
JournalExtreme Mechanics Letters
Early online date20 Oct 2022
Publication statusPublished - 30 Nov 2022


  • Additive manufacturing
  • Ball-and-spring networks
  • Topological softness

ASJC Scopus subject areas

  • Bioengineering
  • Chemical Engineering (miscellaneous)
  • Engineering (miscellaneous)
  • Mechanics of Materials
  • Mechanical Engineering


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