Robust Topological Designs for Extreme Metamaterial Micro-structures

T Chatterjee (Swansea University), S Chakraborty (IIT Delhi, India), S Goswami (Brown University, USA), S Adhikari & MI Friswell (Swansea University)

Nature Scientific Reports, Vol. 11, article 15221, July 2021


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: (i) maximum bulk modulus (ii) maximum shear modulus (iii) minimum negative Poisson's ratio (auxetic metamaterial) and (iv) 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 (i) optimal mean performance (ii) least sensitive design, and (iii) 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.

Paper Availability

This material has been published in Nature Scientific Reports, Vol. 11, article 15221, July 2021, the only definitive repository of the content that has been certified and accepted after peer review. The paper is published as open access.

Link to paper using doi: 10.1038/s41598-021-94520-x

Nature Scientific Reports