Multi-Functional Metamaterials

Optimally designing interdependent mechanical properties in a structure allows for it to be used in application where an arbitrary combination of properties is desired. Architected materials have proven to be an effective way of attaining mechanical behaviors that are unattainable using their constituent materials alone, such as unusual static mechanical properties, unusual wave propagation behavior, and shape morphing. The advent of 3-D printing has allowed for fabricating metamaterials with complex topologies that display engineered mechanics. However, much of the current efforts have focused on optimally designing simple mechanical behaviors such as designing for stiffness and weight, particular frequency bandgaps, or bi-stability. In this work, we study two metamaterial systems where we control and optimize a wide set of static and dynamic properties, and one complex multi-stable structure. Most studies on the optimal design of static properties have focused on engineering stiffness and weight, and much remains unknown about ways to decouple the critical load to failure from stiffness and weight. This is the focus of the first part of our work. We show that the addition of local internal pre-stress in selected regions of architected materials enables the design of materials where the critical load to failure can be optimized independently from the density and/or quasistatic stiffness. We propose a method to optimize the specific load to failure and specific stiffness using sensitivity analysis, and derive the maximum bounds on the attainable properties. We demonstrate the method in a 2-D triangular lattice and a 3-D octahedral truss, showing excellent agreement between experimental and theoretical results. The method can be used to design materials with predetermined fracture load, failure location and fracture paths. For the second part of our work, we focus on designing acoustically transparent structures, by engineering the acoustic impedance -- a combination of wave speed and density, to match that of the surroundings. Owing to the strong correlation between acoustic wave speed and static stiffness, it is challenging to design acoustically transparent materials in a fluid, while maintaining their high structural rigidity. We provide a sensitivity analysis to optimize these properties with respect to design parameters of the structure, that include localized masses at specific positions. We demonstrate the method on five different periodic, three dimensional lattices, to calculate bounds on the longitudinal wave speed as a function of their density and stiffness. We then perform experiments on 3-D printed structures, to validate our numerical simulations. Further, using the sensitivity analysis together with a data-driven approach, we design and demonstrate a mode demultiplexer, that is capable of splitting arbitrarily mixed modes. The tools developed in this work allow for designing structures in a plethora of applications, including ultrasound imaging, wave filtering, and waveguiding. Finally, most multi-stable structures are limited by bi-stability either at the macroscopic or the unit cell level owing to the difficulty in engineering a highly non-linear energy landscape using just elements that display convex energy landscapes. We demonstrate a method to design arbitrarily complex multi-stable shape morphing structures, by introducing rigid kinematic constraints together with disengaging energy storing elements. We present the idea on a kagome lattice configuration, producing a quadri-stable unit cell and complex stable topologies with larger tessellations, validated by demonstrations on 3-D printed structures. Most designs that use passive actuation address one-way shape morphing along the direction of least resistance. We demonstrate reversible, thermally actuated shape morphing between stable open and closed topologies using shape memory springs. The designs can be extended to non-planar structures and fabricated at vastly different length scales.