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Robust topological designs for extreme metamaterial micro-structures.

Tanmoy Chatterjee1, Souvik Chakraborty2, Somdatta Goswami3

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Considering material uncertainty is crucial for designing mechanical metamaterials with extreme properties. Robust optimization improves performance, sensitivity, and elastic characteristics compared to deterministic approaches.

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Area of Science:

  • Materials Science
  • Mechanical Engineering
  • Computational Mechanics

Background:

  • Mechanical metamaterials offer tunable properties.
  • Material uncertainties significantly affect micro-structural design.
  • Topology optimization is key for designing metamaterials.

Purpose of the Study:

  • To investigate the impact of material uncertainty on the topology optimization of mechanical metamaterials.
  • To develop a robust optimization framework for designing metamaterials with extreme mechanical properties.
  • To quantify the benefits of robust design over deterministic design.

Main Methods:

  • Bi-directional evolutionary topology optimization.
  • Energy-based homogenization approach.
  • Parallel Monte Carlo simulations to model material uncertainty (elastic modulus and Poisson's ratio variations).

Main Results:

  • Material uncertainty dramatically influences optimal micro-structural configurations.
  • Robust designs show improved mean performance and reduced sensitivity to variations.
  • Extreme properties achieved include maximum bulk/shear moduli, auxetic behavior, and maximum equivalent elastic modulus.
  • Novel topological patterns emerged for robust extreme material design.

Conclusions:

  • Considering material uncertainty is essential for reliable topology optimization of metamaterials.
  • Robust optimization yields superior mean performance and enhanced stability.
  • The findings provide guidance for designing advanced metamaterials with predictable extreme properties.