The role of electrostriction on the stability of dielectric elastomer actuators

In the field of soft dielectric elastomers, the notion electrostriction indicates the dependency of the permittivity on strain. The present paper is aimed at investigating the effects of electrostriction onto the stability behaviour of homogeneous electrically activated dielectric elastomer actuators. In particular, three objectives are pursued and achieved: i) the description of the phenomenon within the general nonlinear theory of electroelasticity; ii) the application of the recently proposed theory of bifurcation for electroelastic bodies in order to determine its role on the onset of electromechanical and diffuse-mode instabilities in prestressed or prestretched dielectric layers; iii) the analysis of band-localization instability in homogeneous dielectric elastomers. Results for a typical soft acrylic elastomer show that electrostriction is responsible for an enhancement towards diffuse-mode instability, while it represents a crucial property - necessarily to be taken into account - in order to provide a solution to the problem of electromechanical band-localization, that can be interpreted as a possible reason of electric breakdown. A comparison between the buckling stresses of a mechanical compressed slab and the electrically activated counterpart concludes the paper

Optimal energy-harvesting cycles for load-driven dielectric generators in plane strain

The performances of energy harvesting generators based on dielectric elastomers are investigated. The configuration is of a thin dielectric film coated by stretchable electrodes at both sides. The film is first stretched, then charged and subsequently, afterwards it is released, and finally the charge is harvested at a higher electric potential. The amount of energy extracted by this cycle is bounded by the electric breakdown and the ultimate stretch ratio of the film as well as by structural instabilities due to loss of tension. To identify the optimal cycle that complies with these limits we formulate a constraint optimization problem and solve it with a dedicated solver for two typical classes of elastic dielectrics. As anticipated, we find that the performance of the generator depends critically on the ultimate stretch ratio of the film. However, more surprising is our finding of a universal limit on the dielectric strength of the film beyond which the optimal cycle is independent of this parameter. Thus, we reveal that, regardless of how large the dielectric strength of the material is, there is an upper bound on the amount of harvested energy that depends only on the ultimate stretch ratio. We conclude the work with detailed calculations of the optimal cycles for two commercially available elastic dielectrics

Negative refraction for anti-plane elastic waves in canonical quasicrystalline laminates

Elastic anti-plane shear waves can be refracted negatively when they are transmitted across an interface between a homogeneous substrate and a transverse periodic laminate. To achieve pure negative refraction, the frequency of the source should be lower than the upper limit of the second transition zone of the harmonic spectrum of the laminate. An effective way to control the location of transition zones is to consider a canonical configuration for the laminate, a concept that originates from the properties of quasicrystalline sequences among which the Fibonacci one is a particular case. We give a detailed account of the classification in three families of canonical configurations and the role of canonical frequency. We exploit the knowledge of the scaling factor of the self-similar structure of the layout of transition zones for laminates of this kind to provide a quantitative tool to predict the relevant frequencies to accomplish negative refraction. We also investigate how the change of other parameters of the elementary cell may affect the values of those frequencies. The obtained results show that the features of quasicrystalline sequences may be profitably exploited for the realisation of elastic metamaterials

Experimental investigation of the elastoplastic response of aluminum silicate spray dried powder during cold compaction

Mechanical experiments have been designed and performed to investigate the elasto-plastic behaviour of green bodies formed from an aluminum silicate spray dried powder used for tiles production. Experiments have been executed on samples obtained from cold compaction into a cylindrical mould and include: uniaxial strain, equi-biaxial flexure and high-pressure triaxial compression/extension tests. Two types of powders have been used to realize the green body samples, differing in the values of water content, which have been taken equal to those usually employed in the industrial forming of traditional ceramics. Yielding of the green body during compaction has been characterized in terms of yield surface shape, failure envelope, and evolution of cohesion and void ratio with the forming pressure, confirming the validity of previously proposed constitutive models for dense materials obtained through cold compaction of granulates.Comment: 17 pages; Journal of the European Ceramic Society, 201

On the Effect of the Volumetric Deformation in Soft Dielectric Composites with High Phase Contrast

Towards the accurate modelling of soft dielectric composites, this investigation aims at demonstrating that the incompressibility constraint customarily adopted in the literature may lead to largely inaccurate predictions. This claim is grounded on the premise that, even though in these composites each phase may individually be assumed to be incompressible, the volumetric deformation of the softest phase can provide a significant contribution to the effective behaviour if the phase contrast is high enough. To reach our goal, we determine the actuation response of two-phase dielectric laminated composites (DLCs) where the softest phase admits volumetric deformation. Our results, discussed in the light of the limit case in which the softest phase consists of vacuum, on the one hand, challenge the hypotheses usually assumed in the modelling of soft dielectric composites and, on the other hand, are expected to provide useful information for the design of high-performance hierarchical DLCs

On the role of the incompressibility constraint in soft dielectrics

In this work we demonstrate that the incompressibility constraint customarily adopted in literature to model soft dielectric composites may lead to incorrect predictions. In fact, although in these composites each phase may individually be assumed to be incompressible, for high-phase contrast in terms of elastic moduli the volumetric deformation of the softest phase can provide a non-negligible contribution to the effective behaviour. To reach our goal, we determine the effective electric response of a two-phase Dielectric Laminated Composite (DLC) actuator, whose softest phase is described by a constitutive law admitting volumetric deformation. Our results, discussed in the light of the limit case in which the softest phase consists of void, are expected to aid the design of high-performance hierarchical DLCs

Universal Representation of Dynamic Frequency Spectra for Canonical Generalised Quasicrystalline-Generated Waveguides

An effective way to describe the sequence of stop and pass bands in a one-dimensional phononic waveguide is represented by the \lq flow' line reported onto the plot of the relevant $\pi$-periodic reduced torus. In this chapter, these concepts are introduced for silver-mean quasicrystalline-generated elastic waveguides. Results are obtained for canonical configurations for which the dynamic frequency spectra are periodic. Application to finite-size waveguides is also illustrated. As the silver-mean sequence is one of the generalised Fibonacci sequences, the illustrated method can be easily extended to other quasicrystalline substitution rules

Phononic canonical quasicrystalline waveguides

The dynamic behavior of the class of periodic waveguides whose unit cells are generated through a quasicrystalline sequence can be interpreted geometrically in terms of a trace map that embodies the recursive rule obeyed by traces of the transmission matrices. We introduce the concept of canonical quasicrystalline waveguides, for which the orbits predicted by the trace map at specific frequencies, called canonical frequencies, are periodic. In particular, there exist three families of canonical waveguides. The theory reveals that for those (i) the frequency spectra are periodic and the periodicity depends on the canonical frequencies, (ii) a set of multiple periodic orbits exists at frequencies that differ from the canonical ones, and (iii) perturbation of the periodic orbit and linearization of the trace map define a scaling parameter, linked to the golden ratio, which governs the self-similar structure of the spectra. The periodicity of the waveguide responses is experimentally verified on finite specimens composed of selected canonical unit cells

On generalised canonical axial waveguides

The dynamic behaviour of the class of periodic phononic waveguides whose unit cells are generated through a quasicrystalline sequence can be interpreted geometrically in terms of a trace map that embodies the recursive rule obeyed by traces of the transmission matrices. It has been recently shown [1,2] that for a canonical waveguide, the orbits predicted by the trace map at specific frequencies, called canonical frequencies, are periodic onto a surface in a 3D space associated with the invariant of the problem. In this talk, we extend the concept of canonical phononic axial waveguide to generalised Fibonacci sequences and show specific behaviours of the canonical configurations for the so-called silver-mean sequence. We explore various kind of periodic orbits for the trace map associated with different self-similar properties of the stop/pass band layout. The obtained results represent both a key to a better understanding of the dynamic properties of classical two-phase composite waveguides and an important advancement towards the realisation of composite quasicrystalline metamaterials