Soft robots, wearable devices, and energy absorbing systems: these are just examples of a handful of applications in which the fascinating properties of mechanical metamaterials have been utilized. Mechanical metamaterials exhibit properties that are seldom observed in more conventional materials, and these unusual behaviors are governed by the structure and geometry of the system rather than by its composition. Highly nonlinear responses have been demonstrated in mechanical metamaterials, but the computational design of nonlinear systems cannot be easily achieved using established approaches: these systems generally exhibit complex energy landscapes with multiple energy minima, which can be difficult and computationally expensive to navigate. In a recent publication, Bolei Deng, Katia Bertoldi and colleagues introduced an efficient framework for designing mechanical metamaterials with target nonlinear responses.
First, using as a starting point a metamaterial based on hinged rotating squares connected at their vertices, the authors showed that changes in shape of the quadrilateral building units can lead to a range of mechanical responses that result from the rotation of the connected quadrilaterals. The authors explored the behavior of over 7,000 different unit cells of randomly generated quadrilaterals joined at their vertices to identify the key factors that control the mechanical behaviors, including a number of nonlinear stress–strain responses. Next, they developed neural networks to quantify the link between the parameters that describe the geometry of the metamaterials and their nonlinear mechanical responses. The neural network was then combined with an evolution strategy — a stochastic global optimization algorithm based on evolution theory — to identify geometries with target nonlinear mechanical responses. The proposed approach for the inverse design of materials with target properties is more computationally efficient when compared to existing methods that require solving many times the forward problem.
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