Reprogrammable 2D Metamaterials: A Dynamic Approach to Spanning the Eigenvalue Space

Metamaterials, which exhibit unusual macro-behavior determined by their microstructure rather than their chemistry, are an evolving field with potential applications spanning from photonic and phononic bandgaps to auxetics and cloaking. However, designing these materials is a complex process, often requiring specialized expertise, advanced machine learning, or intensive computational algorithms. To address this, we propose an intuitive and streamlined approach to designing 2D mechanical metamaterials by specifically programming degrees of freedom (DOFs) in their construction.<br/>Our method harnesses Straight Line Mechanisms (SLMs) as a single DOF, unimodal material, which can be arranged into specific symmetry patterns (three-way, four-way, and six-way), to sample the entire 2D metamaterial space. The metamaterial's properties can be programmed and reprogrammed by pivoting the mechanism, enabling a dynamic transition through the design space. This approach not only simplifies the design process but also offers adaptability similar to an electronic Field-Programmable Gate Array (FPGA), which can be reprogrammed after manufacturing to perform different tasks, thereby permitting the properties of the metamaterial to be altered and optimized as needed.<br/>We delve into the design space by exploring the available eigenvalues in Cauchy elasticity, which defines the eigenvalue gamut. We further analyze the constraints and unique aspects of the gamut boundaries by probing the space through different symmetry patterns, with and without mirror symmetry, which influences the material's chirality. Moreover, we show the reconfiguration of a single lattice can transition smoothly between extremal properties, showcasing the potency and versatility of our design principle.<br/>Our work provides a novel framework for the creation of reprogrammable, planar mechanical metamaterials. Our strategy facilitates the creation of unique structures like handed shearing auxetics and isotropic materials with Poisson’s ratio approaching +/- 1 and 0. This approach demystifies the complex design process, offering flexibility to span the entire planar elastic tensor space and adapt to varying mechanical needs over time, making it a promising tool for the future of materials science.