UC San Diego

The overarching goal of this dissertation is to exploit the free-hinging motion of mechanism-based, flexible, mechanical metamaterials for designing (1) nonlinear-elastic functional structures and (2) shape morphing. Although there have been many attempts to achieve those unique behaviors by manipulating the chemical composition or microstructure of materials, these approaches are only applicable to a certain class of materials. Meanwhile, mechanical metamaterials exhibit unique behaviors, such as negative Poisson’s ratio or swelling ratio, by harnessing the free-hinging motion and response to mechanical forces (i.e., buckling, snapping, or rotation) of slender elements in their unit cell geometry. In that regard, the goal of this dissertation is to design and control the unit cell geometry of mechanical metamaterials so that they can exhibit unique mechanical behavior without having to modify their chemical composition or microstructure. First, adaptive stiffness metamaterial structures were designed and incorporated in elastic fabric to form next-generation ankle braces so that they enable free movement during low-intensity activities and provide significant biomechanical support during high-intensity activities. Current ankle braces that provide too much support to prevent lateral ankle sprains or reinjury are effective but uncomfortable during normal gait. On the other hand, braces that do not sufficiently support the ankle are comfortable but ineffective. The proposed adaptive stiffness metamaterials, instead, mimic the nonlinear mechanical properties of human ligaments and could provide both comfort and biomechanical support during different intensities of biomechanical movements, which was achieved using their nonlinear-elastic stress-strain properties. To begin, the nonlinear behavior of lateral ankle movements and inversion was investigated through optical motion capture biomechanical and BIODEX tests to identify the strained range and directions around the malleolus during inversion. Adaptive stiffness metamaterials in the form of patterned two dimensional geometries were designed to replicate the nonlinear behavior around the malleolus through parametric optimization. The designed hexagon geometry exhibited load-free shape change like how ligaments behave under low intensity activities until the diagonal elements fully straightened. Thereafter, the straightened elements engaged to bear loads with the material being strained, which resulted in rapid stiffness increase to provide significantly higher biomechanical support during high-intensity activities. The effectiveness of the adaptive stiffness prototype brace was validated through BIODEX tests, and in comparison with other commercial braces. Second, the design principles for these structures to exhibit 2D to 3D morphable behavior when subjected to uniaxial strains were established. Currently, the most common approach is to rely on heterogeneous composite materials and that their anisotropic properties can induce surface morphing. Instead, in this work, the localized compression generated from the free-hinging motion of a re-entrant auxetic geometry was used as a driving force to induce surface morphing in the form of out-of-plane deformations. The geometry was optimized to increase the instability of the geometry, which could lower the critical stress and strain for out-of-plane buckling. In addition, geometrical imperfections were introduced to facilitate controlled surface morphing, inducing programming buckling direction and selective deformations. The lower critical stress and strain also meant that shape morphing could be achieved using soft actuation methods such as pneumatic actuators or stimuli-responsive polymers. To demonstrate this concept, a temperature-responsive nanocomposite hydrogel was integrated with the designed geometries to demonstrate temperature-induced 2D-to-3D shape morphing (and sensing). Overall, this design principle validated that surface morphing could be achieved with a single material and without using anisotropic properties of composite materials. Moreover, this method could be extended to various configurations using other re-entrant auxetic geometries. In summary, the significance of this thesis is that geometrical design enabled the material to attain unique advanced behaviors such as nonlinear elasticity and shape morphing. First, adaptive stiffness metamaterials that behave like human ligaments (i.e., nonlinear-elastic mechanical behavior) was achieved by designing patterned planar structures with embedded free-hinging motion mechanisms. Prototype ankle braces with these embedded metamaterials were designed to exhibit low-stiffness at low-strains before transitioning to high-stiffness at higher-strains. The strain threshold for which stiffness dramatically increases could be precisely designed by tuning the geometric parameters of these materials. The magnitude of the strain threshold is dependent on the ankle region where biomechanical support is needed and was determined from human participant ankle studies. Overall, these metamaterials could be designed to fit any biomechanical brace that require nonlinear elastic supports. Second, the free-hinging motion of a reentrant auxetic geometry was impregnated with designed imperfections to facilitate and control shape morphing response (i.e., patterned out-of-plane deformations) when subjected to in-plane strains. This work is unique because it overcame the limitation of large-arrayed traditional mechanical materials that exhibit unpredictable behavior. The designed imperfections controlled their shape morphing response against external stimuli and made them resistant to manufacturing errors or other load perturbation. In addition, reducing the critical stress and strain enabled the geometry to be actuated through various actuation methods. Overall, these metamaterials could be architected to make exotic 3D configurations using a single elastic material.