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Register a new userTuning Elastic Waves in Soft Phononic Crystal Cylinders via Large Deformation and Electromechanical Coupling
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Soft electroactive materials can undergo large deformation subjected to either mechanical or electrical stimulus, and hence they can be excellent candidates for designing extremely flexible and adaptive structures and devices. This paper proposes a simple one-dimensional soft phononic crystal cylinder made of dielectric elastomer to show how large deformation and electric field can be used jointly to tune the longitudinal waves propagating in the PC. A series of soft electrodes are placed periodically along the dielectric elastomer cylinder, and hence the material can be regarded as uniform in the undeformed state. This is also the case for the uniformly pre-stretched state induced by a static axial force only. The effective periodicity of the structure is then achieved through two loading paths, i.e. by maintaining the longitudinal stretch and applying an electric voltage over any two neighbouring electrodes, or by holding the axial force and applying the voltage. All physical field variables for both configurations can be determined exactly based on the nonlinear theory of electroelasticity. An infinitesimal wave motion is further superimposed on the pre-deformed configurations and the corresponding dispersion equations are derived analytically by invoking the linearized theory for incremental motions. Numerical examples are finally considered to show the tunability of wave propagation behavior in the soft PC cylinder. The outstanding performance regarding the band gap (BG) property of the proposed soft dielectric PC is clearly demonstrated by comparing with the conventional design adopting the hard piezoelectric material. Note that soft dielectric PCs are susceptible to various kinds of failure (buckling, electromechanical instability, electric breakdown, etc.), imposing corresponding limits on the external stimuli.
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Soft materials can be designed with a functionally graded (FG) property for specific applications. In this paper, we analyze the axisymmetric guided wave propagation in a pressurized FG elastomeric hollow cylinder. The cylinder is subjected to a combined action of axial pre-stretch and pressure difference applied to the inner and outer cylindrical surfaces. We consider both torsional waves and longitudinal waves propagating in the FG cylinder made of incompressible isotropic elastomer, which is characterized by the Mooney-Rivlin strain energy function but with the material parameters varying with the radial coordinate in an affine way. The pressure difference generates an inhomogeneous deformation field in the FG cylinder, which dramatically complicates the superimposed wave problem described by the small-on-large theory. A particularly efficient approach is hence employed which combines the state-space formalism for the incremental wave motion with the approximate laminate or multi-layer technique. Dispersion relations for the two types of axisymmetric guided waves are then derived analytically. The accuracy and convergence of the proposed approach is validated numerically. The effects of the pressure difference, material gradient, and axial pre-stretch on both the torsional and the longitudinal wave propagation characteristics are discussed in detail through numerical examples. It is found that the frequency of axisymmetric waves depends nonlinearly on the pressure difference and the material gradient, and an increase in the material gradient enhances the capability of the pressure difference to adjust the wave behavior in the FG cylinder.
A rigid cylinder placed on a soft gel deforms its surface. When multiple cylinders are placed on the surface, they interact with each other via the topography of the deformed gel which serves as an energy landscape; as they move, the landscape changes which in turn changes their interaction. We use a combination of experiments, simple scaling estimates and numerical simulations to study the self-assembly of cylinders in this elastic analog of the Cheerios effect for capillary interactions on a fluid interface. Our results show that the effective two body interaction can be well described by an exponential attraction potential as a result of which the dynamics also show an exponential behavior with respect to the separation distance. When many cylinders are placed on the gel, the cylinders cluster together if they are not too far apart; otherwise their motion gets elastically arrested.
Topological defects (including disclinations and dislocations) which commonly exist in various materials have shown an amazing ability to produce excellent mechanical and physical properties of matters. In this paper, disclinations and dislocations are firstly introduced into the valley-polarized elastic phononic plate. Deformation of the lattice yields the interface expressing as the topologically protected wave guiding, due to the valley-polarized phase transition of phononic crystals (PnCs) across the interface. Then, disclinations are introduced into the Wannier-type elastic phononic plate. The deformation of the lattice yielded by disclinations produces a pentagonal core with the local five-fold symmetry. The topological bound states are well localized around the boundaries of the pentagonal cores with and without the hollow regions. The topological interface state and the topological bound state immunize against the finite sizes and the moderate disturbances of plates, essentially differing from the trivial defect states. The discovery of topological defect states unveils a new horizon in topological mechanics and physics, and it provides a novel platform to implement large-scale elastic devices with robust topological waveguides and resonators.
An instantaneous sub-surface disturbance in a two-dimensional elastic half-space is considered. The disturbance propagates through the elastic material until it reaches the free surface, after which it propagates out along the surface. In conventional theory, the free-surface conditions on the unknown surface are projected onto the flat plane $y = 0$, so that a linear model may be used. Here, however, we present a formulation that takes explicit account of the fact that the location of the free surface is unknown {it a priori}, and we show how to solve this more difficult problem numerically. This reveals that, while conventional linearized theory gives an accurate account of the decaying waves that travel outwards along the surface, it can under-estimate the strength of the elastic rebound above the location of the disturbance. In some circumstances, the non-linear solution fails in finite time, due to the formation of a ``peakon at the free surface. We suggest that brittle failure of the elastic material might in practice be initiated at those times and locations.
Surface waves play important roles in many fundamental and applied areas from seismic detection to material characterizations. Supershear surface waves with propagation speeds greater than bulk shear waves have recently been reported, but their properties are not well understood. In this Letter, we describe theoretical and experimental results on supershear surface waves in rubbery materials. We find that supershear surface waves can be supported in viscoelastic materials with no restriction on the shear quality factor. Interestingly, the effect of prestress on the speed of the supershear surface wave is opposite to that of the Rayleigh surface wave. Furthermore, anisotropy of material affects the supershear wave much more strongly than the Rayleigh surface wave. We offer heuristic interpretation as well as theoretical verification of our experimental observations. Our work points to the potential applications of supershear waves for characterizing the bulk mechanical properties of soft solid from the free surface.
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