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2024
Doctoral Thesis
Title
Design of programmable shape morphing metamaterials
Abstract
In many applications, the shape of a component should ideally adapt to changing boundary conditions instead of being permanently fixed (e.g., in aircraft wings with different flight modes). This would be beneficial to improve energy consumption and to reduce the complexity of systems by reducing components. However, materials research usually aims to develop materials with unchangeable properties that are as stable as possible. The structuring of materials on a µm to cm scale (mesoscale) allows us to design properties such as stiffness and Poisson's ratio by choosing the geometry. In such mechanical metamaterials, unusual values, e.g., negative Poisson's ratio (auxeticity), can be obtained and a specific deformation behavior achieved. These properties define the mechanical deformation behavior and in consequence the shape of the material for a given load. Moreover, the mesostructure can be designed to adjust to external triggers so that the material can adapt to changing conditions. In Programmable Materials, such controlled changes are triggered by stimuli like force, temperature, or a magnetic field. Thus, a predictable behavior can be programmed into materials. It becomes possible, for instance, to store different shapes, and program the overall shape as a function of strain, or logical conditions.
We realized such behavior in unit cells of mechanical metamaterials. Combining many cells allowed us to grade properties and tune specific shape morphing behavior. For this purpose, the distribution of different geometrical parameters (e.g., beam thicknesses, angles) in the material is crucial, which can be manually chosen or determined by mathematical optimization methods. Cells as well as arrays of unit cells were designed using CAD and produced by either 3D printing or foil-stacking. Semi-analytical as well as numerical models were used to characterize them and enable the implementation in a multiscale framework. An experimental validation of the simulated behavior was done by characterizing the shape change of the produced demonstrators. The thesis shows the design process and categorization of Programmable Materials - from unit cells with mechanical mechanisms to macroscopic arrays of unit cells with customized behavior - by means of five unit cells. A honeycomb cell with well-known mechanical behavior is the starting point. We created arrays of these cells and graded the behavior by changing the unit cell’s angle. This allows us to establish curved target shapes for given loads. To achieve a unit cell with changing properties (soft to stiff), we added a stop element (in the form of a single beam) into the cell. Under compression, the beam comes into contact with the cell's edge. In this case, the shape is dependent on external loading and changes in linear steps if different contact gaps are present in the material. On top of that, a novel unit cell that can change between a positive and negative Poisson’s ratio was designed. In combination with a stiffness gradient, the shifting of a bulge through the material to a target position was enabled. The control of multiple geometrical parameters allows to program the way of the morphing independently of the final shape. The fourth unit cell is known from origami. The Miura-Ori cell is auxetic and can be stacked to build a three dimensional structure. The production by foil stacking allows us the generation of a large number of cells in a cheap and simple way. We introduced a parametrization to grade the Poisson’s ratio in all directions. In consequence, we were able to set up a target deformation behavior for an array of unit cells (similar to the honeycomb cell). The last unit cell is a novel design, that leads to a temperature-dependent bistability. The unit cell’s behavior can be switched between a permanent shape change and a complete elastic recovery after removing an applied mechanical load. Additionally, a deformed material can be forced to recover its shape by heating.
We realized such behavior in unit cells of mechanical metamaterials. Combining many cells allowed us to grade properties and tune specific shape morphing behavior. For this purpose, the distribution of different geometrical parameters (e.g., beam thicknesses, angles) in the material is crucial, which can be manually chosen or determined by mathematical optimization methods. Cells as well as arrays of unit cells were designed using CAD and produced by either 3D printing or foil-stacking. Semi-analytical as well as numerical models were used to characterize them and enable the implementation in a multiscale framework. An experimental validation of the simulated behavior was done by characterizing the shape change of the produced demonstrators. The thesis shows the design process and categorization of Programmable Materials - from unit cells with mechanical mechanisms to macroscopic arrays of unit cells with customized behavior - by means of five unit cells. A honeycomb cell with well-known mechanical behavior is the starting point. We created arrays of these cells and graded the behavior by changing the unit cell’s angle. This allows us to establish curved target shapes for given loads. To achieve a unit cell with changing properties (soft to stiff), we added a stop element (in the form of a single beam) into the cell. Under compression, the beam comes into contact with the cell's edge. In this case, the shape is dependent on external loading and changes in linear steps if different contact gaps are present in the material. On top of that, a novel unit cell that can change between a positive and negative Poisson’s ratio was designed. In combination with a stiffness gradient, the shifting of a bulge through the material to a target position was enabled. The control of multiple geometrical parameters allows to program the way of the morphing independently of the final shape. The fourth unit cell is known from origami. The Miura-Ori cell is auxetic and can be stacked to build a three dimensional structure. The production by foil stacking allows us the generation of a large number of cells in a cheap and simple way. We introduced a parametrization to grade the Poisson’s ratio in all directions. In consequence, we were able to set up a target deformation behavior for an array of unit cells (similar to the honeycomb cell). The last unit cell is a novel design, that leads to a temperature-dependent bistability. The unit cell’s behavior can be switched between a permanent shape change and a complete elastic recovery after removing an applied mechanical load. Additionally, a deformed material can be forced to recover its shape by heating.
Thesis Note
Freiburg, Univ., Diss., 2024