Stable propagation of mechanical signals in soft media using stored elastic energy

Abstract

Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals.Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates.soft | mechanical signal | stable propagation | instability S oft, highly deformable materials have enabled the design of new classes of tunable and responsive systems and devices, including bioinspired soft robots (1, 2), self-regulating microfluidics (3), adaptive optics (4), reusable energy-absorbing systems (5, 6), structures with highly programmable responses (7), and morphological computing paradigms (8). However, their highly deformable and dissipative nature also poses unique challenges. Although it has been demonstrated that the nonlinear response of soft structures can be exploited to design machines capable of performing surprisingly sophisticated functions on actuation (1, 2, 9), their high intrinsic dissipation has prevented the design of completely soft machines. Sensing and control functionalities, which require transmission of a signal over a distance, still typically rely on the integration of stiff electronic components within the soft material (10, 11), introducing interfaces that are often a source of mechanical failure.The design of soft control and sensing systems (and, consequently, completely soft machines) requires the ability to propagate a stable signal without distortion through soft media. There are two limiting factors intrinsic to materials that work against this: dispersion (signal distortion due to frequency-dependent phase velocity) and dissipation (loss of energy over time as the wave propagates through the medium). Dispersion can be controlled or eliminated through nonlinear effects produced via the control of structure in the medium (12). For example, periodic systems based on Hertzian contact (13-15), tensegrity structures (16), rigid bars and linkages (17), and bistable elastic elements (18) can behave as nondispersive media, with the nonlinearity of their local mechanical response canceling out the tendency for the signal to disperse at sufficiently large amplitudes. However, dissipation is still an ov...

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

“…Dark-gray regions are unstable by violation of ellipticity, whereas the requirement of positive definiteness further restricts the stable region by also making the light-gray region unstable (the three key inequalities from Eqs. (18) and (23) are shown separately).…”

“…In other words, in the presence of damping, a domain wall will only move in a direction that jumps from a high-energy equilibrium to a low-energy equilibrium. This is of interest for the support of unidirectional wave propagation such as in mechanical diodes [23,267].…”

“…Second, experiments in Ref. [23] used 3D-printing to produce long chains of linear elastically coupled, buckled, bistable beams, see Fig. 21.…”

“…(In)stability is instrumentalized for beneficial material or structural behavior such as, e.g., soft devices undergoing dramatic shape changes [20][21][22], propagating stable signals in lossy media [23] or controlling microfluidics [24], large reversible deformation of cellular solids [25,26], morphing surfaces and structures [27,28], highdamping devices and energy-absorbing technologies from nanotubes to macrodevices [29][30][31][32], acoustic wave guides and metamaterials [33][34][35][36], composites with extreme viscoelastic performance [37][38][39][40], or materials with actively controllable physical properties [41,42]. Especially at the macroscopic level, structural instability and the associated large deformation of soft matter have produced many multifunctional devices that exploit buckling, snapping, and creazing to result in beneficial acoustic or mechanical performance, see Ref.…”

Snap-buckling in asymmetrically constrained elastic strips

“…The bending direction can, however, be reversed by indenting the cylindrical section; the reversal occurs as another elastic instability, called snap-through buckling (or snap buckling). Although snap buckling has a long history of both study and industrial applications, for example, in keyboards and switching devices [36][37][38][39][40][41][42], it is currently receiving increasing attention [43][44][45] in various scientific fields, for example, in studies of mechanical metamaterials [46][47][48][49], small robots [50], or nastic motions in plants [51][52][53][54][55]. To highlight the impact of asymmetric boundary constraints on the mechanics of an elastic geometric structure, here we investigate boundary-driven snap-through buckling of an intrinsically flat elastic strip.…”