Elastic Vector Solitons in Soft Architected Materials

We demonstrate experimentally, numerically, and analytically that soft architected materials can support the propagation of elastic vector solitons. More specifically, we focus on structures comprising a network of squares connected by thin and highly deformable ligaments and investigate the propagation of planar nonlinear elastic waves. We find that for sufficiently large amplitudes two components—one translational and one rotational—are coupled together and copropagate without dispersion. Our results not only show that soft architected materials offer a new and rich platform to study the propagation of nonlinear waves, but also open avenues for the design of a new generation of smart systems that take advantage of nonlinearities to control and manipulate the propagation of large amplitude vibrations.

Figure 1

(a) The system consists of a network of square domains connected by thin ligaments. Pulse waves are generated by a hammer strike on an aluminium impactor and propagate from left to right. (b)–(d) Spatiotemporal displacement diagrams and (c)–(e) spatial displacement profiles at $t=7,10,13,16\mathrm{ms}$ for an impact characterized by (b),(c) $(u_1^{\max },v_1^{\max })=(3.11\mathrm{mm},524\mathrm{mm}/\mathrm{s})$ and (d),(e) $(u_1^{\max },v_1^{\max })=(4.10\mathrm{mm},1166\mathrm{mm}/\mathrm{s})$.

Figure 2

(a) Schematics of the system. (b) Spatial displacement profiles at time $t=9.5\mathrm{ms}$ for five different impacts characterized by different combinations of $u_1^{\max }$ and $v_1^{\max }$. (c) Spatial displacement profiles at $t=6.7$, 10 at 13.3 ms for a single experiment with $(u_1^{\max },v_1^{\max })=(4.10\mathrm{mm},1166\mathrm{mm}/\mathrm{s})$. In (b) and (c) both experimental results (markers) and numerical prediction (blue lines) are shown.

Figure 3

(a) Comparison between analytically (lines) and numerically (markers) predicted normalized displacement and rotation profiles at $T=10$, 20, and 30 and for ${\theta }_0=25°$, $\alpha =1.7$, $K=0.073$. (b) Evolution of $W$ as a function of $A$ and $K$ (assuming ${\theta }_0=25°$ and $\alpha =1.7$). (c) Evolution of $c$ as a function of $A$ and ${\theta }_0$ (assuming $K=0.073$ and $\alpha =1.7$). (d) Evolution of $c$ as a function of $A$ and $K$ (assuming ${\theta }_0=25°$ and $\alpha =1.7$).

Figure 4

Comparison between analytical solution (continuous line) and experimental results (markers). Experimental results are reported for five different impacts characterized by different combinations of $u_1^{\max }$ and $v_1^{\max }$.