Optimizing a reconfigurable material via evolutionary computation

Rapid prototyping by combining evolutionary computation with simulations is becoming a powerful tool for solving complex design problems in materials science. This method of optimization operates in a virtual design space that simulates potential material behaviors and after completion needs to be validated by experiment. However, in principle an evolutionary optimizer can also operate on an actual physical structure or laboratory experiment directly, provided the relevant material parameters can be accessed by the optimizer and information about the material's performance can be updated by direct measurements. Here we provide a proof of concept of such direct, physical optimization by showing how a reconfigurable, highly nonlinear material can be tuned to respond to impact. We report on an entirely computer controlled laboratory experiment in which a $6\times 6$ grid of electromagnets creates a magnetic field pattern that tunes the local rigidity of a concentrated suspension of ferrofluid and iron filings. A genetic algorithm is implemented and tasked to find field patterns that minimize the force transmitted through the suspension. Searching within a space of roughly ${10}^{10}$ possible configurations, after testing only 1500 independent trials the algorithm identifies an optimized configuration of layered rigid and compliant regions.

Figure 1

(a) Picture of the experimental setup, showing the primary components: the linear actuator, the container holding the suspension, and the electromagnet array. The force sensor sits at the bottom of the container. As seen from the side, the container is 1 in. wide and 12 in. tall. (b) Sketch of the side wall of the container, indicating the layout of the magnet array, the size of the impactor at the top, and the position of the force sensor at the bottom. (c) Diagram of the automation process that is run for each configuration tested.

Figure 2

Magnetic field dependence of the viscosity for a 6 cSt ferrofluid, a suspension of 50% by volume 250–400 micron iron filings dispersed in 100 cSt silicone oil, and a suspension of 50% by volume of 250–400 micron iron filings suspended in 6 cSt ferrofluid. The red box indicates the magnetic field $\frac{1}{2}$ in. into the suspension applied by one magnet in the ON state during optimization experiments. The blue box corresponds to the field with the magnet OFF. The nonzero field corresponds to contributions from neighboring magnets turned ON.

Figure 3

(a) Temporal force profile during impact as measured by the sensor at the bottom of the container. The different traces indicate the evolution of the profile during optimization (gray) and in the optimized state (black). The piston impacts the top of the suspension at about $-0.125$ s. (b) Peak force as a function of the number of impacts performed on one fixed configuration without (red) and with (blue) vibration between subsequent impacts. (Inset) Power spectrum of the audio clip used to vibrate the suspension for 30 s between trials.

Figure 4

(a) Median peak force for each generation during a particular optimization run where ten configurations (trials) are tested per generation. The black line is a fit to a decaying exponential, while the red and blue lines correspond to the limit of all magnets ON or OFF, respectively. The pictures indicate the average magnet configuration for a given generation, with color indicating the probability to be ON (black = 100%). Initially all probabilities are about 0.5, but as the optimizer finds better solutions the configurations converge to a particular state. (b) Total error in the median peak force as a function of generation.