Architected metamaterials exhibit complex stress–strain responses, such as quasi-zero stiffness (QZS) plateau response useful in vibration and energy absorption, by exploiting elastic instabilities such as buckling. However, the design of metamaterials with prescribed nonlinear mechanical properties is challenging due to the difficulty in accurately predicting nonlinear mechanical responses such as buckling and self-contact, as well as geometric and material uncertainties. Herein, additive manufacturing (AM) with machine learning (ML) to demonstrate data-driven modeling and the design of nonlinear elastomeric springs with a broad stress plateau is combined. 243 elastomer chi (χ) spring parts with different design parameters fabricated by AM are tested. A Gaussian process (GP) model is trained on key features of the measured mechanical response and predicts the mechanical response within a 3% error with as few as 97 parts. To account for the geometric and material uncertainties, the GP model to develop an uncertainty-aware design optimization approach to tailor the mechanical response based on the covariance matrix adaptation evolution strategy (CMA-ES) is utilized. Excellent agreement is demonstrated between the designed response and measured response over the range of plateau stress considered. The research illustrates the promise of experimental data-driven approaches and AM in enabling complex material design.
Original languageEnglish (US)
Article number2200225
JournalAdvanced Intelligent Systems
Issue number12
StatePublished - Dec 2022


  • additive manufacturing
  • machine learning
  • energy absorption
  • elastomers
  • design optimizations
  • buckling


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