Gal Shmuel

Band-gaps in electrostatically controlled dielectric laminates subjected to incremental shear motions

Abstract The thickness vibrations of a finitely deformed infinite periodic laminate made out of two layers of dielectric elastomers is studied. The laminate is pre-stretched by inducing a bias electric field perpendicular to the layers. Incremental time-harmonic fields superimposed on the initial finite deformation are considered next. Utilizing the Bloch-Floquet theorem along with the transfer matrix method we determine the dispersion relation which relates the incremental fields frequency and the phase velocity. Ranges of frequencies at which waves cannot propagate are identified whenever the Bloch-parameter is complex. These band-gaps depend on the phases properties, their volume fraction, and most importantly on the electric bias field. Our analysis reveals how these band-gaps can be shifted and their width can be modified by changing the bias electric field. This implies that by controlling the electrostatic bias field desired frequencies can be filtered out. Representative examples of laminates with different combinations of commercially available dielectric elastomers are examined.

The Rayleigh–Lamb wave propagation in dielectric elastomer layers subjected to large deformations

The propagation of waves in soft dielectric elastomer layers is investigated. To this end incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined. First we examine the case of mechanically traction free layer, which is an extension of the Rayleigh–Lamb problem in the purely elastic case. Two other loading configurations are accounted for too. Subsequently, numerical examples for the dispersion relations are evaluated for a dielectric solid governed by an augmented neo-Hookean strain energy. It is found that the phase speeds and frequencies strongly depend on the electric excitation and pre-stretch. These findings lend themselves at the possibility of controlling the propagation velocity as well as filtering particular frequencies with suitable choices of the electric bias field.

Axisymmetric wave propagation in finitely deformed dielectric elastomer tubes

Wave propagation in hollow dielectric elastomer cylinders is studied. The quasi-static deformation of the tube owing to a combination of radial electric field and mechanical loading is determined first. Two combinations are accounted for, one at which the tube is free to expand in the axial direction, and another at which the tube is axially pre-stretched and restricted from elongating. Subsequently, longitudinal axisymmetric incremental motions are superposed on the underlying state. The governing equations in the tube and in the surrounding space are formulated and a numerical procedure is used in order to solve the resulting set of equations. The fundamental mode in the frequency spectrum is determined for thin, intermediate and thick wall tubes. The influences of the tube geometry, the mechanical pre-stretch and particularly the electric bias field are examined. An important observation is the ability to manipulate the propagation of the waves by adjusting the electromechanical bias field. This infers the use of dielectric elastomers in tubular configurations as active waveguides or isolators by a proper tuning of the electrostatic stimuli.

Applications of Wavelets in the Representation and Prediction of Transformation in Shape‐Memory Polycrystals

In recent years, new developments in materials characterization techniques have led to a vast amount of data on the microstructure of polycrystals. Simultaneously, nimprovements in computational capabilities have enabled accurate full-field simulations for the micro-mechanical fields developing in polycrystalline aggregates. These show that in phenomena including phase transformation, localized bands of deformation percolate in a complex way across various grains. Our objective is to develop a methodology for analyzing, storing and representing microstructure ndata and, in turn, to identify the relevant information dictating the macroscopic behavior in superelastic polycrystals. To this end, wavelets are used in a case nstudy of a polycrystalline aggregate in anti-plane shear. It is demonstrated how the transformation fields developing within the material can be efficiently represented by thresholding their wavelet expansion, maintaining more than 90% of the L_2 norm of the original field, while using approximately 10% of the number of terms in the original data. The macroscopic stress-strain relation resulting from nsolving the governing equations using a thresholded transformation strain is shown to be in a good agreement with the exact relation. Finally, the set of the functions nretained in the expansion after thresholding was found to be similar in adjacent loading steps. Motivated by these observations, we propose a new wavelet-based algorithm for calculating the developing fields in phase transforming polycrystals.