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Biological materials such as seashell nacre exhibit extreme mechanical properties due to their multilayered microstructures. Collaborative interaction among these layers achieves performance beyond the capacity of a single layer. Inspired by these multilayer biological systems, we architect materials with free-form layered microstructures to program multistage snap-buckling and plateau responses—accomplishments challenging with single-layer materials. The developed inverse design paradigm simultaneously optimizes local microstructures within layers and their interconnections, enabling intricate layer interactions. Each layer plays a synergistic role in collectively achieving high-precision control over the desired extreme nonlinear responses. Through high-fidelity simulations, hybrid fabrication, and tailored experiments, we demonstrate complex responses fundamental to various functionalities, including energy dissipation and wearable devices. We orchestrate multisnapping phenomena from complex interactions between heterogeneous local architectures to encode and store information within architected materials, unlocking data encryption possibilities. These layered architected materials offer transformative advancements across diverse fields, including vibration control, wearables, and information encryption. 

Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the corresponding topological bands. However, among the vast number of theoretically predicted topological states, only a small fraction has been physically realized. To close this gap, we present a strategy capable of systematically and efficiently discovering metamaterials with desired topological state. Our approach builds on topological quantum chemistry, which systematically classifies topological states by analyzing symmetry properties at selected wavevectors. Because this method condenses the topological character into mathematical information at a small set of wavevectors, it encodes a clear and computationally efficient objective for topology optimization algorithms. We demonstrate that, for certain lattice symmetries, this classification can be further reduced to intuitive morphological features of the phonon band structure. By incorporating these band morphology constraints into topology optimization algorithms and further fabricating obtained designs, we enable the automated discovery and physical realization of metamaterials with targeted topological properties. This methodology establishes a paradigm for engineering topological elastic lattices on demand, addressing the bottleneck in material realization and paving the way for a comprehensive database of topological metamaterial configurations. 

Abstract The properties of materials and structures typically remain fixed after being designed and manufactured. There is a growing interest in systems with the capability of altering their behaviors without changing geometries or material constitutions, because such reprogrammable behaviors could unlock multiple functionalities within a single design. We introduce an optimization-driven approach, based on multi-objective magneto-mechanical topology optimization, to design magneto-active metamaterials and structures whose properties can be seamlessly reprogrammed by switching on and off the external stimuli fields. This optimized material system exhibits one response under pure mechanical loading, and switches to a distinct response under joint mechanical and magnetic stimuli. We discover and experimentally demonstrate magneto-mechanical metamaterials and metastructures that realize a wide range of reprogrammable responses, including multi-functional actuation responses, adaptable snap-buckling behaviors, switchable deformation modes, and tunable bistability. The proposed approach paves the way for promising applications such as magnetic actuators, soft robots, and energy harvesters. 

We envision programmable matters that can alter their physical properties in desirable manners based on user input or autonomous sensing. This vision motivates the pursuit of mechanical metamaterials that interact with the environment in a programmable fashion. However, this has not been systematically achieved for soft metamaterials because of the highly nonlinear deformation and underdevelopment of rational design strategies. Here, we use computational morphogenesis and multimaterial polymer 3D printing to systematically create soft metamaterials with arbitrarily programmable temperature-switchable nonlinear mechanical responses under large deformations. This is made possible by harnessing the distinct glass transition temperatures of different polymers, which, when optimally synthesized, produce local and giant stiffness changes in a controllable manner. Featuring complex geometries, the generated structures and metamaterials exhibit fundamentally different yet programmable nonlinear force-displacement relations and deformation patterns as temperature varies. The rational design and fabrication establish an objective-oriented synthesis of metamaterials with freely tunable thermally adaptive behaviors. This imbues structures and materials with environment-aware intelligence. 

Abstract Buckling, a phenomenon historically considered undesirable, has recently been harnessed to enable innovative functionalities in materials and structures. While approaches to achieve specific buckling behaviors are widely studied, tuning these behaviors in fabricated structures without altering their geometry remains a major challenge. Here, we introduce an inverse design approach to tune buckling behavior in magnetically active structures through the variation of applied magnetic stimuli. Our proposed magneto-mechanical topology optimization formulation not only generates the geometry and magnetization distribution of these structures but also informs how the external magnetic fields should be applied to control their buckling behaviors. By utilizing the proposed strategy, we discover magnetically active structures showcasing a broad spectrum of tunable buckling mechanisms, including programmable peak forces and buckling displacements, as well as controllable mechano- and magneto-induced bistability. Furthermore, we experimentally demonstrate that multiple unit designs can be assembled into architectures, resulting in tunable multistability and programmable buckling sequences under distinct applied magnetic fields. By employing a hybrid fabrication method, we manufacture and experimentally validate the generated designs and architectures, confirming their ability to exhibit precisely programmed and tunable buckling behaviors. This research contributes to the advancement of multifunctional materials and structures that harness buckling phenomena, unlocking transformative potential for various applications, including robotics, energy harvesting, and deployable and reconfigurable devices.