Figure 1

(Color online) (a) Experimental setup showing the diamond shaped guide and indicating the number of beads composing each portion of the system. (b) Schematic of the composition of a particle with an embedded piezogauge.Reuse & Permissions

Figure 2

(Color online) Highly nonlinear waves propagating in the Y-shape guide composed of all stainless steel particles. (a) Experimental data corresponding to the transformation of a solitary wave excited by an identical steel striker traveling at $\sim 0.585\text{m}/\text{s}$ in the first horizontal branch. The $y$-axes scale is 2.5 N per division. (b) Corresponding numerical results. The $y$-axes scale is 2.5 N per division.Reuse & Permissions

Figure 3

(Color online) Trains of highly nonlinear waves propagating in uniform systems composed of all PTFE and all stainless steel beads showing the experimental (a,c) and corresponding numerical data (b,d). In the latter, the curves plotted correspond to the same sensor position as in experiments. (a) Waves excited by a 0.45 g striker in a PTFE based system at $\sim 0.25\text{m}/\text{s}$ impact velocity. The $y$-axes scale for all curves is 0.2 N per division. (b) Numerical simulations corresponding to (a). The $y$-axes scale for all curves is 0.5 N per division. (c) Waves excited by a 5.33 g steel striker in a stainless steel based system at $\sim 0.18\text{m}/\text{s}$. The $y$-axes scale for the top curve is 2 N per division and 1 N per division for the other curves. (d) Numerical simulations corresponding to (c). The $y$-axes scale for all curves is 5 N per division. The curve with the fastest impulse propagation corresponds to the signal recorder from the branch composed of steel beads. The top curves are shifted on different divisions to ease readability. (e) Density plots of numerically computed particle forces (N) in the subsystem of Figs. 3c, 3d composed of stem 1–steel branch (either branch 1 or branch 2, due to symmetry) and stem 2 (full steel system). The horizontal axis is labeled according to particle site along each branch and the vertical axis gives the time step number (each time $\text{step}=3\times {10}^{-6}\text{s}$).Reuse & Permissions

Figure 4

(Color online) Highly nonlinear waves propagating in the diamond-shaped holder having one of the branches filled with PTFE beads and the rest of the structure composed of stainless steel particles. (a) Experimental data corresponding to the transformation of a solitary wave excited by a 0.45 g striker traveling at $\sim 0.20\text{m}/\text{s}$ in the first horizontal branch. The $y$-axes scale for the top two curves is 2 N per division, while it is 0.2 N per division for the two lower curves. (b) Corresponding numerical results. The $y$-axes scale is 2 N per division except for the third curve from the top (green) where it is 0.4 N per division. The curve with the fastest impulse propagation corresponds to the signal recorder from the branch composed of steel beads. The top curves are shifted on different divisions to ease readability. (c) Density plots of numerically computed particle forces (N) in the subsystem of Figs. 4a, 4b composed of stem 1–PTFE branch and stem 2. The horizontal axis is labeled according to particle site along each branch and the vertical axis gives the time step number (each time $\text{step}=3\times {10}^{-6}\text{s}$).Reuse & Permissions

Figure 5

(Color online) Highly nonlinear waves propagating in the diamond-shaped holder having one of the branches filled with Parylene-C coated steel beads and the rest of the structure composed of bare stainless steel particles. System excited by a 0.45 g striker traveling at $\sim 0.50\text{m}/\text{s}$. (a) Experimental data, the $y$-axes scale is 2 N for the two top most curves, 0.4 N per division for the third curve and 0.1 N for the bottom curve. (b) Numerical simulations, the $y$-axis scale is 5 N per division for the two topmost curves, 1.25 N for the third (green) and 2.5 N for the bottom (red) curve. The curve with the fastest impulse propagation corresponds to the signal recorder from the branch composed of steel beads. The top curves are shifted on different divisions to ease readability. (c) Density plots of numerically computed particle forces (N) in the subsystem of Figs. 5a, 5b composed of stem 1–Parylene-C coated branch and stem 2. The horizontal axis is labeled according to particle site along each branch and the vertical axis gives the time step number (each time $\text{step}=3\times {10}^{-6}\text{s}$).Reuse & Permissions

Figure 6

(Color online) Highly nonlinear waves propagating in the diamond-shaped holder having one of the branches filled with Parylene-C coated steel beads and the rest of the structure composed of bare stainless steel particles. System excited by a 5.33 g striker traveling at $\sim 0.35\text{m}/\text{s}$. (a) Experimental data, the $y$-axes scale for the three topmost curves is 5 N per division and 0.5 N per division for the last (bottom) curve. (b) Numerical simulations, the $y$-axis scale is 10 N for all curves except the bottom (red) curve that is 5 N. The curve with the fastest impulse propagation corresponds to the signal recorder from the branch composed of steel beads. The top curves are shifted on different divisions to ease readability. (c) Density plots of numerically computed particle forces (N) in the subsystem of Figs. 6a, 6b composed of stem 1–Parylene-C coated branch and stem 2. The horizontal axis is labeled according to particle site along each branch and the vertical axis gives the time step number (each time $\text{step}=3\times {10}^{-6}\text{s}$).Reuse & Permissions

Figure 7

Schematic showing the notation used in the numerical modeling.Reuse & Permissions