Wave management in 1D and 2D granular systems: designs for stress wave mitigation and control

Controlling stress waves during impact beyond merely dissipating their energy through material fracture, fragmentation, yielding etc., has been a significant focus of research in recent years. Materials exhibiting stress wave control characteristics would enable novel applications, such as for example stress wave focusing, deflection, annihilation, etc. that otherwise may not be present. Ordered granular media are one material group that has shown promise in this respect as they have been shown, at least in the elastic range, to possess very different wave propagation properties than continuous solids, such as the ability to sustain solitary waves – constant width and shape but variable speed waves. This dissertation investigates several granular systems, based on metallic spherical granules, that have been designed specifically to study certain aspects of wave propagation management. The first portion of this work investigates manipulating wave propagation in 1D granular chains. One design is easily altered between two configurations by a slight tilt in a gravitational field, and acts as a switch for wave propagation with peak amplitude on the order 10s of N: in one configuration, a solitary wave passes through unaltered, while in the other configuration, the travelling wave is significantly attenuated. A second design acts as a low pass force filter for high amplitude solitary waves (10s of kN) which is achieved through the use of preconditioned contacts – a process in which the granule contacts are loaded (beyond yield) to some peak force prior to use such that no further plasticity will occur in situ if the peak amplitude of the propagating wave is less than the peak preconditioning load. The second portion of this work investigates elasto-plastic wave propagation in 2D granular square and hexagonal packings. The input wave experiences significant dissipation within as few as five contacts due to plastic dissipation at the granule contacts. The wave propagation patterns are determined to be similar to their elastic counterparts. The diameter tolerance is determined to be a primary source of scatter in the data. The final part of this dissertation suggests designs to tailor the wave propagation within a granular packing. A numerical optimization scheme is utilized to determine the placement of cylindrical intruders at select interstitial locations within a square packing to accomplish momentum or force maximizations/minimizations at certain regions in the packing. The numerical and experimental results are similar with respect to the wave arrival time and peak forces experienced at certain locations within the packing. Several configurations demonstrate the ability to tailor the wave propagation in the granular packing through the use of interstitial cylinders, which laterally couple the square system. For some optimization scenarios, the numerical scheme does not outperform the baseline test cases. Thus, an iterative scheme is developed by forbidding intruders at certain locations, in effect changing the initial conditions of the optimization problem, and rerunning the optimization. The iterative scheme is shown to improve the results of the optimization. A second method of tailoring elasto-plastic wave propagation is by preconditioning select contacts within a hexagonal packing. Depending on the orientation of the preconditioned contacts, the wave can be laterally deflected or allowed to pass through the packing with less attenuation. Interfacial packings, in which only a portion of the packing has preconditioned contacts, clearly illustrate the effect of the preconditioned contacts on the wave propagation behavior