A particularly interesting avenue to tune the properties of mechanical metamaterials has been to harness instabilities. These instabilities can be used to increase the sensitivity to external loads, and enable multistability and hysteretic behavior. In contrast to the complex and unstable behavior that these mechanical metamaterials show, their architecture is often surprisingly simple. One of the iconic examples is an elastomeric material patterned with a square lattice of circular pores. Upon compression, a collective buckling instability suddenly changes the Poisson’s ratio from positive to negative, and in a similar fashion changes e.g. the phononic behavior by opening and closing band gaps. While several studies focus on the effects of pore shape and pore distribution, the mechanical properties have only been tuned within limits dictated by a few geometrical parameters.

Here, design optimization approaches could play a key role in solving the inverse problem: to design mechanical metamaterials with specific properties, and explore the bounds of achievable functionality. Importantly, most of the algorithms use gradient information of the objective function and constraints to  reach a local or global minimum, which limits the applicability of these optimization methods. To that end, the Soft Robotic Matter Group developed a stochastic topology optimization strategy based on simulated annealing that does not require gradient information, to inversely design periodic structures with targeted buckling behavior. To reduce the search space and to generate smooth structures, we have introduced a heuristic subroutine inspired by the ferromagnetic Ising model. We show that it is possible to design structures with maximum buckling load, but also allow tailoring to a predefined buckling force within a wide range of values. We furthermore show that by controlling the occurrence of higher modes, we can effectively remove multi‐mode interactions that occur for nearly degenerate bifurcations. Such an approach is not limited to mechanical problems, as also shown by a collaboration where we optimize the behavior of 2D diffraction-based overlay metrology targets.

Röhrich, R., Oliveri, G., Kovaios, S., Tenner, V., Den Boef, A., Overvelde, J. T. B., Koenderink, A. F., (2020). Uncertainty Estimation and Design Optimization of 2D Diffraction-based Overlay Metrology Targets. ACS Photonics. [web]

Oliveri, G.Overvelde, J.T.B., (2020). Inverse Design of Mechanical Metamaterials that Undergo Buckling. Advanced Functional Materials. [web]