Phonon controlled mechanical memory via pinning and depinning of transition waves

Abstract

Multistable mechanical metamaterials enable programmable transitions between discrete stable states through propagating kink transition waves (TWs). Yet controlling these kinks typically requires local actuation or high-energy deformation, limiting scalability. Here we demonstrate a universal strategy for pinning and depinning TWs using local defects and boundary phonon excitations. Inspired by phonon-dislocation interactions in crystalline solids, we use pairs of phonons that form a beating envelope resonant with the pinned kink's translational mode, which lies within a phononic band gap. This resonant coupling efficiently transfers energy to the kink, allowing it to overcome defect barriers and propagate across impurities. The proposed mechanism enables application of these systems as information processing units in mechanical computing, namely as scalable and more robust mechanical memory.

Figures (19)

• Figure 1: (a) Possible mechanical realization of the system, with bistable beams coupled by springs, with defect at the center. (b) Symmetric and asymmetric potentials $V(u)$. (c) Transition wave displacement profile, for different asymmetries $\alpha$. (d) Threshold value $\epsilon_{min}$ for various damping coefficients, at different $\alpha$. (e) TW passes through a defect which $\epsilon/\epsilon_{min}<1$, and (f) is pinned if $\epsilon/\epsilon_{min}\geq1$.
• Figure 2: (a) Dispersion relation of the system. (b) Beating perturbation as seen from a unit far before the pinned kink. The two separate phonons are indicated in light blue and the beating that they generate in dark blue. (c) Spectrum of the localized and extended modes of the pinned kink. In green the translational T-mode (low frequency) and in red the internal I-mode, in dark blue the extended modes. $\epsilon<0.3\epsilon_{min}$ defects are not able to statically hold the kink (showing $\omega_T=0$). (d) The I-mode and (e) T-mode shape (left) and the displacement perturbation they cause with different intensities $a_J$ (right); the dashed curves correspond to the unperturbed kink when $a_J=0$. A second-order discontinuity in the shape mode can be seen at $x-x_d=0$ because of the defect.
• Figure 3: (a) Harmonic potential of the linear ROM (light blue) compared to the potential energy of the kink quasi-particle (dark blue) (b) Comparison between simulation and non-linear ROM where high-amplitude excitations cause depinning. (c) Softening frequency response of the non-linear ROM for amplitudes just lower than depinning (0.125), showing two peaks at $0.4\omega_T$ and $0.85\omega_T$. (d) Simulations showing the frequency and amplitude dependence of depinning. (e) A system with two defects (at units 100 and 225), in which a TW is stopped and depinned twice. (f) System with array of defects ($\epsilon < \epsilon_{min}$); the TW passes through them until slowed down by a timed excitation (single beat), gets pinned, and subsequently depinned using beating phonons.
• Figure S1: Schematics of the discrete system from Eq. \ref{['eq:SIinitialeq']}.
• Figure S2: Elastic energy, analytical form from Eq. \ref{['eq:SIEe']} compared to the full simulation (using Matlab's ode45). Here it's possible to see how, by refining the simulations with higher densities of points (reducing the spacing $a_s$), as explained before in SI Section 2, the results always match well the simulations results, without the difference that a strongly discrete system would introduce.