Massimiliano Gei

Standards for dielectric elastomer transducers

Dielectric elastomer transducers consist of thin electrically insulating elastomeric membranes coated on both sides with compliant electrodes. They are a promising electromechanically active polymer technology that may be used for actuators, strain sensors, and electrical generators that harvest mechanical energy. The rapid development of this field calls for the first standards, collecting guidelines on how to assess and compare the performance of materials and devices. This paper addresses this need, presenting standardized methods for material characterisation, device testing and performance measurement. These proposed standards are intended to have a general scope and a broad applicability to different material types and device configurations. Nevertheless, they also intentionally exclude some aspects where knowledge and/or consensus in the literature were deemed to be insufficient. This is a sign of a young and vital field, whose research development is expected to benefit from this effort towards standardisation.

Band-gap shift and defect-induced annihilation in prestressed elastic structures

Design of filters for electromagnetic, acoustic, and elastic waves involves structures possessing photonic/phononic band gaps for certain ranges of frequencies. Controlling the filtering properties implies the control over the position and the width of the band gaps in question. With reference to piecewise homogeneous elasticbeams on elastic foundation, these are shown to be strongly affected by prestress (usually neglected in these analyses) that (i) “shifts” band gaps toward higher (lower) frequencies for tensile (compressive) prestress and (ii) may “annihilate” certain band gaps in structures with defects. The mechanism in which frequency is controlled by prestress is revealed by employing a Green’s-function-based analysis of localized vibration of a concentrated mass, located at a generic position along the beam axis. For a mass perturbing the system, our analysis addresses the important issue of the so-called effective negative mass effect for frequencies within the stop bands of the unperturbed structure. We propose a constructive algorithm of controlling the stop bands and hence filtering properties and resonance modes for a class of elastic periodic structures via prestress incorporated into the model through the coefficients in the corresponding governing equations.

Controlling Bandgap in Electroactive Polymer-Based Structures

A waveguide with a periodic structure is able to filter waves whose frequencies lie in the band-gap ranges displayed in dispersion diagrams. The lengths of these forbidden bands depend on the contrast in material and geometrical properties of parts of the system which realize the periodicity. In this paper, a novel way to control band gaps is proposed: to set the geometric characteristics of a prestretched waveguide made of soft dielectric elastomer applying an external voltage to pairs of electrodes applied with a regular pattern on the device. The technique proves to be feasible and is able to tune accurately the position of band gaps over all frequency spectrum. For the investigated system, a device able to guide flexural waves, bandgap ranges of about 100-200 Hz have been obtained over frequencies on the order of 1 kHz.

Transformation elastodynamics and cloaking for flexural waves

The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general form of the partial differential equation is not invariant with respect to the cloaking transformation. The significant result of this paper is the analysis of the transformed equation and its interpretation in the framework of the linear theory of pre-stressed plates. The paper provides a formal framework for transformation elastodynamics as applied to elastic plates. Furthermore, an algorithm is proposed for designing a broadband square cloak for flexural waves, which employs a regularised push-out transformation. Illustrative numerical examples show high accuracy and efficiency of the proposed cloaking algorithm. In particular, a physical configuration involving a perturbation of an interference pattern generated by two coherent sources is presented. It is demonstrated that the perturbation produced by a cloaked defect is negligibly small even for such a delicate interference pattern.

An Interface Model for the Periodontal Ligament

A nonlinear interface constitutive law is formulated for modeling the mechanical behavior of the periodontal ligament. This gives an accurate interpolation of the few available experimental results and provides a reasonably simple model for mechanical applications. The model is analyzed from the viewpoints of both mathematical consistency and effectiveness in numerical calculations. In order to demonstrate the latter, suitable two- and three-dimensional nonlinear interface finite elements have been implemented.

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.

Bifurcations of a coated, elastic cylinder

Bifurcations in velocities from a state of homogeneous axisymmetric deformation are investigated for a coated elastic cylinder subject to axial tension or compression. The cylinder and the finite-thickness coating have circular cross sections. At the coating/core contact, a linear interface is introduced to simulate imperfect bonding. The particular case in which the thickness of the coating becomes infinite is also addressed. This may model the behaviour of a fiber embedded in an infinite matrix. Generic modes of bifurcations are investigated in the elliptic range, comprised axi- and anti-symmetric modes. Incompressible, hyperelastic materials, including Ogden, Mooney–Rivlin, and J2-deformation theory of plasticity, are considered in the applications.

Performance of soft dielectric laminated composites

This paper contains a thorough investigation of the performance of electrically activated layered soft dielectric composite actuators under plane deformation. Noting that the activation can be induced by controlling either the voltage or the surface charge, the overall behaviour of the system is obtained via homogenization at large strains, taking either the macroscopic electric field or the macroscopic electric displacement field as independent electrical variables. The performance of a two-phase composite actuator compared to that of the homogeneous case is highlighted for few boundary-value problems and for different values of stiffness and permittivity ratios between constituents being significant for applications, where the soft matrix is reinforced by a relatively small volume fraction of a stiff and high-permittivity phase. For charge-controlled devices, it is shown that some composite layouts admit, on one hand, the occurrence of pull-in/snap-through instabilities that can be exploited to design release-actuated systems, and on the other hand, the possibility of thickening at increasing surface charge density.

Analysis of viscoelastic soft dielectric elastomer generators operating in an electrical circuit

A predicting model for soft dielectric elastomer generators (DEGs) must consider a realistic model of the electromechanical behaviour of the elastomer filling, the variable capacitor and of the electrical circuit connecting all elements of the device. In this paper such an objective is achieved by proposing a framework for reliable simulations of soft energy harvesters. In particular, a simple electrical circuit is realised by connecting the capacitor, stretched periodically by a source of mechanical work, in parallel with a battery through a diode and with an electrical load consuming the energy produced. The electrical model comprises resistances simulating the effect of the electrodes and of the conductivity current invariably present through the dielectric film. As these devices undergo a high number of electro-mechanical loading cycles at large deformation, the time-dependent response of the material must be taken into account as it strongly affects the generator outcome. To this end, the viscoelastic behaviour of the polymer and the possible change of permittivity with strains are analysed carefully by means of a proposed coupled electro-viscoelastic constitutive model, calibrated on experimental data available in the literature for an incompressible polyacrylate elastomer (3M VHB4910). Numerical results showing the importance of time-dependent behaviour on the evaluation of performance of DEGs for different loading conditions, namely equi-biaxial and uniaxial, are reported in the final section.

Thermoelastic small-amplitude wave propagation in nonlinear elastic multilayers

A framework for thermoelastic analysis of wave propagation in multilaminated structures is given. The elastic material is subject to an arbitrary, homogeneous deformation and to a condition of uniform temperature. Small-amplitude vibrations are analyzed starting from this state, in a fully coupled thermomechanical formulation.