Nonlinear deformation analysis of a dielectric elastomer membrane–spring system

Abstract

Due to their large strain capability, dielectric elastomers are promising materials for application as transducers in cameras, robots, valves, pumps, energy harvesters, and so on. The dielectric elastomer transducers are based on the deformation of a soft polymer membrane contracting in thickness and expanding in area, induced by the application of a voltage across the two compliant electrodes coated on both sides of the membrane. This paper focuses on the static large deformation analysis of a dielectric elastomer membrane-spring system. The system is constructed from attaching a disk in the middle of a circular dielectric membrane and then connecting the disk with a spring. This configuration can be potentially used as a key part in valves. The basic governing equations describing the large out-of-plane deformations are formulated, and the obtained equations are solved numerically. The relations related to the displacement of the disk, the spring force, the applied voltage, and the parameters of spring including stiffness and initial length are illustrated. The results show that the anticipated displacement of the disk can be controlled by adjusting either or both of the parameters of the spring and the applied voltage. In addition, the parameters of the spring, that is, the stiffness and the initial length, play an important role in the performance of the membrane-spring system.

Performance Optimization of a Conical Dielectric Elastomer Actuator

“…After the out-of-plane deformation, a particle on the membrane at radius R in Figure 3i now occupies the position of (r(R), z(R)), where r is the current radius and z is the distance to the undeformed plane. The coordinates of (r, z) for R = [a, b] describe the geometry of the conical DEA shape, and are developed as follows (after [26]). To describe the free energy density W as well as s1 and s2, the Ogden model [31] was adopted in this work, which is given as…”

“…As has been pointed out by [24,25], the simplifying assumption of a truncated cone shape becomes less valid when the ratio of the inner disk radius to outer ring radius, a/b, becomes smaller, which leads to a greater error in model prediction. A quasi-static analytical model for conical DEA which is based on thermodynamic equilibrium and geometry relationships was developed in [26]. This model is capable of capturing the nontruncated membrane shape and the inhomogeneous stress distribution.…”

“…In the following sections, we first present a modified analytical model adopted from [26] which can characterize the quasi-static force-displacement relationship of a conical DEA at an applied voltage. We then present experiments to verify this model and identify the model parameters.…”

Highly deformable actuators made of dielectric elastomers clamped by rigid rings

“…[20][21][22][23][24] Here we use a variational principle to derive the equations of equilibrium, and adopt a specialized numerical method taking advantage of axisymmetric shape of the curved membranes. [25][26][27][28][29] An actuator is made of a membrane of a dielectric elastomer sandwiched between two soft conductors of negligible stiffness. In the reference state (Fig.…”

Modeling and control of innovative smart materials and actuators: A tutorial

“…Several DEAP models have been proposed in literature for describing the static and the dynamic response, respectively by means of hyperelasticity theory [37], [38], energetic approaches [39], [40], and viscoelasticity theory [41]- [43]. A physics-based model for the case of an annular DEAP membrane can be found in [44], and is reported in condensed form in (17), where the input is the voltage u, the output is the displacement d (see Fig.…”