Combinatorics

Physics

Finite element method

Topology (electrical circuits)

Homogenization (climate)

Mathematics

Structural engineering

Biology

Poisson distribution

Parametric statistics

Statistical physics

Statistics

Mathematical optimization

Biodiversity

Metamaterial

Machine learning

Poisson's ratio

Engineering

Composite material

Optimal design

Ecology

Topology optimization

Materials science

Modulus

Monte Carlo method

Computer science

Optoelectronics

Auxetics

Scientific Reports

We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical properties of metamaterials. The algorithm is based on the bi-directional evolutionary topology optimization and energy-based homogenization approach. To simulate additive manufacturing uncertainty, combinations of spatial variation of the elastic modulus and/or, parametric variation of the Poisson’s ratio at the unit cell level are considered. Computationally parallel Monte Carlo simulations are performed to quantify the effect of input material uncertainty to the mechanical properties of interest. Results are shown for four configurations of extreme mechanical properties: (1) maximum bulk modulus (2) maximum shear modulus (3) minimum negative Poisson’s ratio (auxetic metamaterial) and (4) maximum equivalent elastic modulus. The study illustrates the importance of considering uncertainty for topology optimization of metamaterials with extreme mechanical performance. The results reveal that robust design leads to improvement in terms of (1) optimal mean performance (2) least sensitive design, and (3) elastic properties of the metamaterials compared to the corresponding deterministic design. Many interesting topological patterns have been obtained for guiding the extreme material robust design.

Robust topological designs for extreme metamaterial micro-structures