Atul Kumar Sharma

Abstract: This paper reports a finite element based numerical framework for simulating the electromechanical behavior of nonlinear anisotropic dielectric elastomer actuators at finite strains. Based on the existing models for incompressible anisotropic neo-Hookean hyperelastic solids and ideal dielectric elastomers, a theory of anisotropic dielectric elastomers is outlined. The analytical expressions are derived for the tangent moduli of the anisotropic materials. A computationally efficient staggered solution algorithm is presented for solving the coupled nonlinear equations by decoupling displacement and electric potential fields. Selective reduced integration technique is used for alleviating the volumetric locking due to material incompressibility. The model is implemented into an in-house finite element program. We first validate the accuracy of the finite element implementation by considering the cases of homogeneous deformation, with a particular emphasis on the electromechanical instability. Subsequently we demonstrate the utility of the proposed numerical framework by analyzing two representative cases (bending and buckling actuators) involving inhomogeneous deformations. In both the cases, anisotropy in the mechanical properties of the elastomer is found to have a favorable influence on the actuation performance. Finally, for various mesh sizes, a comparison of the computation time required by the monolithic solution approach and the proposed staggered approach is presented to highlight the computational efficacy of the latter.

Abstract: This paper reports an energy-based method for the dynamic pull-in instability analysis of a spherical dielectric elastomer (DE) balloon subjected to a quasi-statically applied inflation pressure and a Heaviside step voltage across the balloon wall. The proposed technique relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle, followed by the imposition of an instability condition for extracting the threshold parameters. The material models of the Ogden family are employed for describing the hyperelasticity of the balloon. The accuracy of the critical dynamic pull-in parameters is established by examining the saddle-node bifurcation in the transient response of the balloon obtained by integrating numerically the equation of motion, derived using the Euler–Lagrange equation. The parametric study brings out the effect of inflation pressure on the onset of the pull-in instability in the DE balloon. A quantitative comparison between the static and dynamic pull-in parameters at four different levels of the inflation pressure is presented. The results indicate that the dynamic pull-in instability gets triggered at electric fields that are lower than those corresponding to the static instability. The results of the present investigation can find potential use in the design and development of the balloon actuators subjected to transient loading. The method developed is versatile and can be used in the dynamic instability analysis of other conservative systems of interest.

Abstract: Electrically driven dielectric elastomers (DEs) suffer from an electromechanical instability (EMI) when the applied potential difference reaches a critical value. A majority of the past investigations address the mechanics of this operational instability by restricting the kinematics to homogeneous deformations. However, a DE membrane comprising both active and inactive electric regions undergoes inhomogeneous deformation, thus necessitating the solution of a complex boundary value problem. This paper reports the numerical and experimental investigation of such DE actuators with a particular emphasis on the EMI in quasistatic mode of actuation. The numerical simulations are performed using an in-house finite element framework developed based on the field theory of deformable dielectrics. Experiments are performed on the commercially available acrylic elastomer (VHB 4910) at varying levels of prestretch and proportions of the active to inactive areas. In particular, two salient features associated with the electromechanical response are addressed: the effect of the flexible boundary constraint and the locus of the dielectric breakdown point. To highlight the influence of the flexible boundary constraint, the estimates of the threshold value of potential difference on the onset of electromechanical instability are compared with the experimental observations and with those obtained using the lumped parameter models reported previously. Additionally, a locus of localized thinning, near the boundary of the active electric region, is identified using the numerical simulations and ascertained through the experimental observations. Finally, an approach based on the Airy stress function is suggested to justify the phenomenon of localized thinning leading to the dielectric breakdown.

Abstract: The paper presents a Hamiltonian approach for extracting the dynamic instability parameters of homogeneously deforming dielectric elastomer actuators subjected to an unequal biaxial prestress, and driven by a suddenly applied electric load. The approach relies on setting up the balance between the kinetic, strain, and electrostatic energy at the point of maximum overshoot in an oscillation cycle. The equation of the stagnation curve, obtained by invoking aforestated statement of energy-balance, is operated upon by the condition of instability to determine the instability parameters. The underlying principles of the approach are elucidated by considering the Ogden family of hyperelastic material models. The approach is however portrayed generically, and hence, can be extended to the other hyperelastic material models of interest. The estimates of the dynamic instability parameters are corroborated by examining the saddle-node bifurcation points in the time-history response obtained by integrating the equation of motion. A parametric study is conducted to bring out the effect of unequal biaxial prestress, and the trends of variation of the critical electric field and the thickness-stretch on the onset of dynamic instability are presented. A quantitative comparison with the static instability parameters reveals that the dynamic instability gets triggered for electric fields that are lower than those corresponding to the static instability. In contrast, the maximum stretch experienced by the actuator at the dynamic instability is significantly higher than that at the static instability. The crucial inferences can find their potential use in the design of DEAs subjected to a transient motion.

Abstract: for the force on a dielectric in an electrical field E and bounded by a surface S with unit normal n. He used an operational \"definition\" of stress and concluded that the compensating mechanical forces which must be introduced operationally are not derivable from a tensor. It is suggested here that Slepian's analysis is essentially correct and that the difficulty arises because of the choice of an operationally \"defined\" stress. This choice is inconsistent with the existence of an electrical surface stress-which is familiar, in the magnetic analogue, in studies of the form effect-and it is argued here that the Euler-Cauchy definition of stress is the appropriate one. The Definition of Stress.-In authoritative works on continuum mechanics stress is introduced by means of the stress hypothesis of Euler and Cauchy,2 that is, by asserting that, acting upon any imagined closed geometrical surface a within the body, there exists a field of stress vectors t which has an equivalent effect to the (interparticle) forces exerted by the material outside aupon the material within. For a dielectric material the interaprticle (i.e., intermolecular) forces are partly long-range in character and they may therefore contribute not only to t but also to f, the body force per unit volume. For the present purpose, however, the important point to note is that ais an imagined geometrical surface and not a physical surface of separation within the material. An alternative procedure is to use the operational definition of stress in which it is imagined that a physical cut is made in the material along an internal element of surface dd = nda. If means are then introduced for keeping the strains in the material on both sides of the cut the same as they were before the cut was made, then the force introduced by these means is t'do-, where t' is the operationally defined stress vector. In adopting this operational definition, Slepian commented: \"It is not assumed that the cut and the introduced means do not disturb the microstructure and micromechanics of the material. For example, in the case of a fluid the cut and means would cause molecules to be reflected which would otherwise pass through the geometric element of surface dS. It is assumed, however, that in spite of the change in the micromechanics, there is no change in the observable macromechanics.\"' It may also be noted there is a further element of idealization involved in that the cut is imagined to be of finite extent: in practice, as discussed later in this paper, it is only possible to measure the force on an element of volume when the element is completely separated from the rest of the body. For an ordinary elastic material the stress acting at a physical surface of separa-

Abstract: Dielectric elastomer transducers are often subject to large tensile stretches and are susceptible to rupture. Here we carry out an experimental study of the rupture behavior of membranes of an acrylic dielectric elastomer. Pure-shear test specimens are used to measure force-displacement curves, using samples with and without pre-cracks. We find that introducing a pre-crack into a membrane drastically reduces the stretch at rupture. Furthermore, we measure the stretch at rupture and fracture energy using samples of different heights at various stretch-rates. The stretch at rupture is found to decrease with sample height, and the fracture energy is found to increase with stretch-rate.

Abstract: : A hydrostatically coupled dielectric elastomer (HCDE) actuator consists of two membranes of a dielectric elastomer, clamped with rigid circular rings. Confined between the membranes is a fixed volume of a fluid, which couples the movements of the two membranes when a voltage or a force is applied. This paper presents a computational model of the actuator, assuming that the membranes are neo-Hookean, capable of large and axisymmetric deformation. The voltage-induced deformation is described by the model of ideal dielectric elastomer. The force is applied by pressing a rigid flat punch onto one of the membranes over an area of contact. The computational predictions agree well with experimental data. The model can be used to explore nonlinear behavior of the HCDE actuators.

Abstract: The basic modern theory of nonlinear electroelasticity and its use in the formulation of constitutive laws governing the behaviour of dielectric elastomer materials was summarized in a recent revie...