<p>In shock absorbing applications foams are often used for their unique stiffness properties. Polymer foams exhibit non-linear stiffness regions during cell buckling. Non-linear stiffness behavior, especially quasi-zero stiffness and negative stiffness, is ideal for shock absorption and vibration attenuation applications for two main reasons: non-linear stiffness regions extend the force deflection curve, creating more energy absorbed, without large changes in reaction forces, thus maximizing the energy absorbed per force generated; nonlinear stiffness regions can prevent physical waveforms from propagating through the material by providing internal vibration modes and vanishing material moduli.</p><p>This work attempts to create a 2-dimensional metamaterial from a tessellation of 0-dimensional unit cells composed of one or more Chi-springs and nodal connection material. Multiple tessellation concepts are proposed and analyzed with regard to their effectiveness in preserving the Chi-spring ideal non-linear behavior in the 2-D array, as well as stability, spacial efficiency, and compressibility ratios. A tessellation must be stable throughout its compression cycle, exhibit some form of non-linear behavior and have a reasonable spacial efficiency and compressibility to advance the Chi-spring based metamaterial into two dimensions. Beginning at the tessellation unit cells, the non-linear behavior is affected because the individual Chi-springs are no longer loaded directly over their center in the vertical direction. This changes the proportions of deflection modes of the chi-springs, due to the presence of transverse components of loads and internal moments. The tessellations are intended to respond to loads in any direction and multi-directional loads, as these types of loading scenarios are common in the potential applications for such a metamaterial. Not only will these tessellations not behave isotopically, but the behavior in one direction may be dependent on the load and/or deflection in other directions, based on changes in internal geometry during deflection. This concept of inter-directional interference patterns is unique to each tessellation. Methods of changing the geometry of the tessellations parametrically and biasing the axes angles or nodal spacing can be used to optimize their behavior.</p>

The Effectiveness of 2D Unit Cells in Creating χ-Spring Based Metamaterials

Paper Proceedings: https://asmedigitalcollection.asme.org/SMASIS/SMASIS2021/volume/85499

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