Neuromorphic metamaterial structures

Abstract Computerized structural optimization methods are often used to design the shape of structures to achieve a desired function, such as a specific compliance. In the simplest case of a structure built from a material with small deformations obeying Cauchy elasticity, the compliance is constant and the relationship between the forces applied on the structure and its deformation is linear. This linearity severely limits the types of functions which can be achieved by such materials. Here we study mechanical metamaterials made of repeating unit cells, each with specific dimensional parameters and with one-sided contact non-linearities. We show that the force and displacement equilibrium configurations of these metamaterials are mathematically equivalent to the fixed points of a recurrent artificial neural network. By exploiting this equivalence, we demonstrate mechanical metamaterials that can be designed (trained) to implement complex non-linear functions, using a gradient descent algorithm as in artificial neural networks. One of our metamaterial structures has a higher compliance when it is pressed against a pattern of raised bumps corresponding to the vowels in the Braille alphabet, than when it is pressed against patterns for six consonants. As artificial neural networks are known to be efficient models for numerous problems in machine learning, our results reveal that beneficial features of neural networks can be transferred to physical objects (mechanical structures). These features include the design of systems with complex input–output relationships by using generic methods that only rely on the repetitive processing of pairs of inputs and desired outputs, as well as remarkable generalization capabilities. We anticipate our methodology to be a starting point for the transfer of some of the breakthroughs in the rapidly advancing field of machine learning to highly functional physical devices in applications that are constrained by energy, volume, data processing or response time.