Learning to learn by using nonequilibrium training protocols for adaptable materials.

Evolution in time-varying environments naturally leads to adaptable biological systems that can easily switch functionalities. Advances in the synthesis of environmentally responsive materials therefore open up the possibility of creating a wide range of synthetic materials which can also be trained for adaptability. We consider high-dimensional inverse problems for materials where any particular functionality can be realized by numerous equivalent choices of design parameters. By periodically switching targets in a given design algorithm, we can teach a material to perform incompatible functionalities with minimal changes in design parameters. We exhibit this learning strategy for adaptability in two simulated settings: elastic networks that are designed to switch deformation modes with minimal bond changes and heteropolymers whose folding pathway selections are controlled by a minimal set of monomer affinities. The resulting designs can reveal physical principles, such as nucleation-controlled folding, that enable such adaptability.

Reprogrammable allosteric metamaterials from disordered networks.

Prior works on disordered mechanical metamaterial networks-consisting of fixed nodes connected by discrete bonds-have shown that auxetic and allosteric responses can be achieved by pruning a specific set of the bonds from an originally random network. However, bond pruning is irreversible and yields a single bulk response. Using material stiffness as a tunable design parameter, we create metamaterial networks where allosteric responses are achieved without bond removal. Such systems are experimentally realized through variable stiffness bonds that can strengthen and weaken on-demand. In a disordered mechanical network with variable stiffness bonds, different subsets of bonds can be strategically softened to achieve different bulk responses, enabling a multiplicity of reprogrammable input/output allosteric responses.

Auxetic metamaterials from disordered networks.

Recent theoretical work suggests that systematic pruning of disordered networks consisting of nodes connected by springs can lead to materials that exhibit a host of unusual mechanical properties. In particular, global properties such as Poisson's ratio or local responses related to deformation can be precisely altered. Tunable mechanical responses would be useful in areas ranging from impact mitigation to robotics and, more generally, for creation of metamaterials with engineered properties. However, experimental attempts to create auxetic materials based on pruning-based theoretical ideas have not been successful. Here we introduce a more realistic model of the networks, which incorporates angle-bending forces and the appropriate experimental boundary conditions. A sequential pruning strategy of select bonds in this model is then devised and implemented that enables engineering of specific mechanical behaviors upon deformation, both in the linear and in the nonlinear regimes. In particular, it is shown that Poisson's ratio can be tuned to arbitrary values. The model and concepts discussed here are validated by preparing physical realizations of the networks designed in this manner, which are produced by laser cutting 2D sheets and are found to behave as predicted. Furthermore, by relying on optimization algorithms, we exploit the networks' susceptibility to tuning to design networks that possess a distribution of stiffer and more compliant bonds and whose auxetic behavior is even greater than that of homogeneous networks. Taken together, the findings reported here serve to establish that pruned networks represent a promising platform for the creation of unique mechanical metamaterials.

Designing allostery-inspired response in mechanical networks.

Recent advances in designing metamaterials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally efficient approach, we extend this idea to tune more general properties of networks. With nearly complete success, we are able to produce a strain between any two target nodes in a network in response to an applied source strain on any other pair of nodes by removing only ∼1% of the bonds. We are also able to control multiple pairs of target nodes, each with a different individual response, from a single source, and to tune multiple independent source/target responses simultaneously into a network. We have fabricated physical networks in macroscopic 2D and 3D systems that exhibit these responses. This work is inspired by the long-range coupled conformational changes that constitute allosteric function in proteins. The fact that allostery is a common means for regulation in biological molecules suggests that it is a relatively easy property to develop through evolution. In analogy, our results show that long-range coupled mechanical responses are similarly easy to achieve in disordered networks.

Ideal isotropic auxetic networks from random networks.

Auxetic materials are characterized by a negative Poisson's ratio, ν. As the Poisson's ratio approaches the lower isotropic mechanical limit of ν = -1, materials show enhanced resistance to impact and shear, making them suitable for applications ranging from robotics to impact mitigation. Past experimental efforts aimed at reaching the ν = -1 limit have resulted in highly anisotropic materials, which show a negative Poisson's ratio only when subjected to deformations along specific directions. Isotropic designs have only attained moderately auxetic behavior or have led to solutions that cannot be manufactured in 3D. Here, we present a design strategy to create isotropic structures from disordered networks, which result in Poisson's ratios as low as ν = -0.98. The materials conceived through this approach are successfully fabricated in the laboratory and behave as predicted. ν depends on network structure and bond strengths; this sheds light on the motifs which lead to auxetic behavior. The ideas introduced here can be generalized to 3D, a wide range of materials, and a spectrum of length scales, thereby providing a general platform that could impact technology.

Designing the pressure-dependent shear modulus using tessellated granular metamaterials.

Jammed packings of granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus 〈G〉 increases as a power law in pressure p for static packings of soft spherical particles that can rearrange during compression. We seek to design granular materials with shear moduli that can either increase or decrease with pressure without particle rearrangements even in the large-system limit. To do this, we construct tessellated granular metamaterials by joining multiple particle-filled cells together. We focus on cells that contain a small number of bidisperse disks in two dimensions. We first study the mechanical properties of individual disk-filled cells with three types of boundaries: periodic boundary conditions (PBC), fixed-length walls (FXW), and flexible walls (FLW). Hypostatic jammed packings are found for cells with FLW, but not in cells with PBC and FXW, and they are stabilized by quartic modes of the dynamical matrix. The shear modulus of a single cell depends linearly on p. We find that the slope of the shear modulus with pressure λ_{c}<0 for all packings in single cells with PBC where the number of particles per cell N≥6. In contrast, single cells with FXW and FLW can possess λ_{c}>0, as well as λ_{c}<0, for N≤16. We show that we can force the mechanical properties of multicell granular metamaterials to possess those of single cells by constraining the end points of the outer walls and enforcing an affine shear response. These studies demonstrate that tessellated granular metamaterials provide a platform for the design of soft materials with specified mechanical properties.

Directed aging, memory, and nature's greed.

Disordered materials are often out of equilibrium and evolve very slowly in a rugged and tortuous energy landscape. This slow evolution, referred to as aging, is deemed undesirable as it often leads to material degradation. However, we show that aging also encodes a memory of the stresses imposed during preparation. Because of inhomogeneous local stresses, the material itself decides how to evolve by modifying stressed regions differently from those under less stress. Because material evolution occurs in response to stresses, aging can be "directed" to produce sought-after responses and unusual functionalities that do not inherently exist. Aging obeys a natural "greedy algorithm" as, at each instant, the material simply follows the path of most rapid and accessible relaxation. Our experiments and simulations illustrate directed aging in examples in which the material's elasticity transforms as desired because of an imposed deformation.