<p>Structures with inherent shape change capabilities enable adaptive, efficient designs without the weight and complexity of external actuators and sensors. Morphing structures are found in nature: plants are able to achieve fast motion without muscular or nervous systems. For example, the Venus flytrap snaps to a closed state with spatially distributed curvatures in less than one second. In contrast, synthetic shape change has been limited by a trade-off between complexity and speed. Shape memory polymers (SMPs) can remember complex shapes, but morphing is slow and one-way. Multistability due to mechanical buckling is fast and reversible, but it has been limited to simple shapes. Furthermore, many examples of biological shape change follow logical patterns with mechanisms that selectively respond to environmental stimuli. This suggests that synthetic morphing structures may also lend themselves to alternative forms of sensing, memory, and logic.</p> <p><br></p> <p>In this research, we introduce a new method of using SMPs in combination with the hierarchical architectures of pre-strained multistable laminates to create switchable multistable structures (SMS). An SMS can remember multiple permanent shapes and reversibly snap between them. We use extrusion-based 3D printing to encode contrasting shape memory-based pre-strain fields in a bilayer. Above the SMP’s glass transition temperature, the SMS becomes compliant and remembers multiple encoded permanent shapes with fast snap-through between them. Below the transition temperature, the SMS regains its stiffness and is fixed in a single state. The geometric freedom of 3D printing enables the design and manufacture of bioinspired structures with complex pre-strain fields and deflections. The developed printing method is applied in multiple subsequent studies, including mechanical pixels, self-folding spring origami structures, and multistable structures printed with thermoset composite inks. </p> <p><br></p> <p>The highly nonlinear behavior of bistable, pre-strained structures makes their design difficult and nonintuitive. Generally, these structures are designed using a slow, iterative process with finite element analysis (FEA). We aim to solve the inverse optimization problem: start with target stable states and solve for the necessary pre-strain distributions. To this end, we develop and implement the switching tunneling method (STM) to design pre-strained,</p> <p>multistable structures. Instead of FEA, we leverage analytical solutions for gradient-based optimization. Tunneling allows for the efficient search of a design space which may contain multiple local and global minima. Switching enables us to take advantage of two different function transformations, depending on if the search is far from or close to a minimum. The STM is validated through FEA and experiments for both conventional and variable</p> <p>pre-strain bistable structures.</p> <p><br></p> <p>Structures designed to react to external conditions or events offer the opportunity to directly integrate sensing, memory, and computation into a structure. This concept is explored using metasheets composed of locally bistable unit cells, which display spatiotemporal mechanical sensing (mechanosensing) and memory. A unit cell consists of a bistable dome with a piezoresistive strip at the base; the resistance indicates the state of the dome. The mechanics of bistability offer inherent filtering and nonlinear signal amplification capabilities, tunable via geometric parameters. Metasheet arrays of these unit cells display distributed sensing capabilities, as well as hierarchical multistability.</p> <p><br></p> <p>We explore the use of time-dependent material properties combined with the mechanics of multistability to encode many unique values within a single mechanosensor unit cell, beyond binary memory. When the piezoresistive material is viscoelastic, cyclic loading causes cumulative changes in both the ground and inverted state resistances. Effectively, the metamaterial is able to count how many times an external force has been applied; this count is stored in the metamaterial’s intrinsic, measurable properties.</p> <p><br></p> <p>This work demonstrates the importance of incorporating memory concepts into structural design, which enables multistability with complex stable shapes, as well as spatiotemporal sensing and memory capabilities. Engineered systems require increasingly adaptive and responsive structures to improve efficiency. The incorporation of inherent memory and sensing enables the complex behaviors needed to interact with unstructured environments</p> <p>and biological features, a pressing issue for aerospace, soft robotics and biomedical devices. The methodology developed here to manufacture, design, and analyze multistable structures advances the state of the art and makes their implementation more practical.</p>

<p dir="ltr">Vibration is ubiquitous in the modern world, making it a topic that cannot be avoided during design, manufacture, and maintenance. Systems, such as civil structures and suspension of cars, are normally designed to stay in the attenuation zone to avoid harsh vibrations. Designing and manufacturing systems with the desired natural frequency distribution is easy. However, it is much harder to maintain the frequency response since materials keep aging as time goes by. To counter the effect of aging and attenuate vibrations, this thesis designed a meta-material that is capable of reprogramming its natural frequency distribution by inserting various masses at different locations. This ability to specifically adjust the system's natural frequency distribution is what we define as "Digital Inertia Programming".</p><p dir="ltr">The model consists of 12 identical unit cells, with each unit cell comprising two types of springs. By determining whether to insert a mass into the unit cell at various locations, the model achieves its programmability to adjust its natural frequency distribution. A "Binary Representation" is used to label the patterns of mass inserted in the model. Each unit cell is represented by a binary bit and a total of 12 bits are used to indicate the presence of mass in each unit cell. In the thesis, we mainly discuss bilaterally symmetrical patterns to avoid unwanted twisting. For the 12 unit cells, we can obtain a total of 128 bilaterally symmetrical patterns, resulting in 896 independent natural frequencies for the model. The number of patterns and independent natural frequencies will increase exponentially with the increase of the number of unit cells in the model.</p><p dir="ltr">An ideal one-dimensional analytical metamaterial model is developed. Lagrange's method is used to determine the system's mass matrix and stiffness matrix directly from the kinetic energy and potential energy equations. The natural frequencies and mode shapes are then calculated from the eigenvalue equation. Based on free response analysis and sensitivity analysis, the model successfully showed great programmability on frequency distribution by varying the insert patterns, as well as changing the value of the variables in the model, such as the weight of the inserts, the weight of the top mass, the stiffness of the unit cell wall spring and the stiffness of the connecting spring. When continuously varying the parameter, the model's natural frequency distribution also changes continuously, giving a possibility to adjust the natural frequency distribution by carefully adjusting the weight of the mass inserted at each location. Lastly, a forced-response analysis is performed, and the amplitude of the model's frequency response is plotted. This provides a straightforward view of the changes in the band gaps and the overall stiffness of the model by altering the patterns with two inserts.</p><p dir="ltr">A two-dimensional model is developed based on the one-dimensional model. The model retains the same 12 unit cells setup as the one-dimensional model. Aiming to ensure stability, the rectangular-shaped unit cell is now configured as a combination of two triangles. Taylor expansion and small angle approximation are used to eliminate nonlinear terms and triangular function terms in the stiffness matrix respectively. The model again shows its programmability by adjusting the variables of the model. Since the results of asymmetrical patterns are bounded by the results of symmetrical patterns, including the asymmetrical patterns increases the model's precision. However, the symmetrical patterns already provide a good representation of the model. The rotational motion is added to the inserts in the model, which further increases the model's complexity. In the model, the mode shapes are characterized by the rotational motion of inserts and the horizontal motion of inserts, which correspond to a zero strain mode of the model. A linear regression model is trained based on 100 bilaterally symmetrical patterns to predict the second lowest natural frequencies of the two-dimensional model for both symmetrical and asymmetrical patterns. The success in the linear regression model indicates the potential for applying machine learning algorithms to the design of meta-materials in the future.</p>