Effect of humidity on the static–dynamic electromechanical performance of viscoelastic dielectric elastomers in pure shear state

Subject to a mechanical load or a voltage, a membrane of a dielectric elastomer deforms. As for the deformation mode, the dynamic performance and stability are strongly affected by how mechanical forces are applied. In the current study, by using the Euler-Lagrange equation, an analytical model is developed to characterize the dynamic performance of a homogeneously deformed viscoelastic dielectric elastomer under the conditions of equal-biaxial force, uniaxial force, and pure shear state, respectively. Numerical results are shown to describe the electromechanical deformation and stability. It is observed that the resonant frequency (where the amplitude-frequency curve peaks) has dependencies on the deformation mode, the level of mechanical load, and the applied electric field. When a dielectric elastomer membrane is subject to equal-biaxial force or pure shear state, it undergoes a nonlinear quasi-periodic vibration. An aperiodic motion of the dielectric elastomer system is induced by the boundary condition of a uniaxial force.

Analytically described polynomial yield criterion by considering both plane strain and pure shear states

Although stress and strain states are same in simple and pure shear states, longitudinal wave velocity changes propagating in the plastically deformed medium under simple and pure shear states are apparently different each other according to authors' theoretical and experimental research works. The objective of this paper is to discuss the effect on ultrasonic wave velocity changes due to texture and cross slip under simple and pure shear states via finite element polycrystal analysis. In small plastic deformation range, in spite of quite different longitudinal wave velocity changes under simple and pure shear states, the texture developments and transverse wave velocity changes under both states are similar each other. That suggests dependence of transverse wave velocity on texture. Next, the multiplicative amounts of intersected slides between primary and secondary slip systems, which relates closely to the amount of cross slip, under simple and pure shear states are examined. The result, i.e., this multiplicative amount under pure shear state is larger than that under simple shear state, means the point defects induced by cross slip are much easier to introduce under pure shear state than under simple shear state and suggests that the point defects induced by cross slip may cause quite different longitudinal wave velocity changes.

Dielectric elastomers (DEs) under pure shear state can generate the giant deformation without the pull-in and snap-through instabilities. The pure shear state is usually achieved by using fibers to constrain the deformation in an in-plane direction. Since the DEs cannot support the compressed stress, the instability of loss of tension (LT) may occur in the fiber-constrained direction as the voltage-induced Maxwell stress increases. In this article, by incorporating the effects of different values of tensile force, applied voltage (including both step and ramp voltages), prescribed constrained deformation and viscoelasticity intensity, a viscoelastic model is employed to explore the instability of LT of fiber-constrained DEs with analysis of the electromechanical deformation and stress evolution.

In-plane torsion test has attracted a lot of attention recently. As a novel shear test, it can avoid unwanted reaction torque compared with the traditional in-plane shear test. The in-plane torsion test with circular groove specimens can avoid early fracture at the free edges, and thus achieve actual fracture strain under pure shear state because it has no free boundaries. In this study, digital image correlation is implemented to measure the torsion angle to obtain the precise torque-torsion angle curves. For specimens with slits, strain hardening is calibrated by inverse engineering approach. The strain path at the center of the shear zone during the torsion test is observed to be very close to a pure simple shear state. Cyclic shear loading tests are carried out for twin bridge shear specimen. The combined isotropic-nonlinear kinematic hardening model, Yoshida–Uemori two-surface model, and homogeneous anisotropic hardening model are evaluated to characterize the cyclic loading behaviors.KeywordsBauschinger effectCyclic shear loadingIn-plane torsion testKinematic hardeningDistorted hardening

In the authors' previous study, velocity changes of ultrasonic waves under simple and pure shear states were studied both theoretically and experimentally. The research work revealed the quite different longitudinal wave velocity changes between under the simple and pure shear states and also distinguished longitudinal velocity change under the pure shear state, on the other hand transverse wave velocity changes under simple and pure shear states showed almost the same change tendencies similar to the texture development under both shear states. Therefore, to clear the different effects due to plastic deformation on transverse and longitudinal waves velocity changes under simple and pure shear states the microstructural changes of polycrystal solids were investigated via finite element polycrystal model (FEPM). The analyzed results suggested that the transverse wave velocity depends upon texture developments mainly, whereas the longitudinal wave velocity depends heavily upon point defects induced by intersected cross slips among dislocations. The principal object of this paper is experimental verification of point defects dependence of the longitudinal wave velocity using a pure Aluminum single crystal. As a result, no point defects occurring under single slip stage was simulated by FEM analysis for crystal plasticity and experimental evidence of no longitudinal wave velocity changes under same stage was shown. It was confirmed that the longitudinal waves velocity depends under the point defects.

Although stress and strain states are same in simple and pure shear states, longitudinal wave velocity changes propagating in the plastically deformed medium under simple and pure shear states are apparently different each other as the results of authors' theoretical and experimental research works. The objective of this paper is to discuss the effect on ultrasonic wave velocity changes due to texture and cross slip under simple and pure shear states via finite element polycrystal analysis. First the texture developments under both states are studied and the results suggest the dependence of transverse wave velocity changes on texture in the small plastic deformation range. Next, the multiplicative amounts of intersected slids between primary and secondary slip systems, which relates closely to the amount of cross slip under both states are calculated and the results show that the point defects induced by cross slip are much easier to be introduced under pure shear state than that under simple shear state, this suggests that the point defects induced by cross slip may cause quite different longitudinal wave velocity changes.

We address the effects of various deformation modes, equibiaxial tension, uniaxial tension and pure shear on the energy diagrams and stability restrictions of a dielectric elastomer (DE) generator. It is shown that the stability restrictions, as well as the maximum energy that can be converted, are deformation-dependent. DE generators working under the pure shear state can avert electromechanical instability provided that tensile stress prevails over the membrane. The energy output in the pure shear state is lower than that of equibiaxial tension, but much higher than that of uniaxial tension.

When a continuum approach is considered for textile reinforcements, the internal loads are described by a stress tensor. The mechanical behaviour of the textile material is very much dependent on the fiber directions, and the frames defined from warp and weft directions are preferred to write the stress components. The exterior loads in these frames permit to define tensile and pure shear states. Nevertheless, these frames are generally not orthogonal. The relationships between the exterior loads and the different stress components are analyzed in the present paper, and, in particular, the relationship between direct stress components and longitudinal loads on one hand, and shear stress components and transversal loads on the other hand. When dealing with textile materials, the exterior loads in the direction of the fibres and transverse to the fibres define the pure tensile and pure shear state. It is shown that the covariant stress component matrix is diagonal in a pure tensile loading and that the first mixed direct stress components are equal to zero in a pure shear loading. In these cases, the direct relationship between the stresses and the loadings are given. This is applied to the cases of the picture frame test, the biaxial tensile test or of a combined tension-shear test.

When a continuum approach is considered for textile reinforcements, the internal loads are described by a stress tensor. The mechanical behaviour of the textile material is very much dependent on the fiber directions, and the frames defined from warp and weft directions are preferred to write the stress components. The exterior loads in these frames permit to define tensile and pure shear states. Nevertheless these frames are generally not orthogonal. The relationships between the exterior loads and the different stress components are analyzed in the present paper, and, in particular, the relationship between direct stress components and longitudinal loads on one hand, and shear stress components and transversal loads on the other hand. When dealing with textile materials, the exterior loads in the direction of the fibres and transverse to the fibres define the pure tensile and pure shear state. It will be shown that the covariant stress component matrix is diagonal in a pure tensile loading and that the first mixed direct stress components are equal to zero in a pure shear loading. In these cases, the direct relationship between the stresses and the loadings are given. This will be applied to the cases of the picture frame test, the biaxial tensile test or of a combined tension-shear test.

Ultrasonic nondestructive material evaluation method and study on texture and cross slip effects under simple and pure shear states

It is well known that a state of pure shear has distinct sets of basis vectors or coordinate systems: the principal axes, in which the stress is diagonal, and pure shear bases, in which diag(stress)=0. The latter is commonly taken as the definition of pure shear, although a state of pure shear is more generally defined by tr(stress)=0. New results are presented that characterize all possible pure shear bases. A pair of vector functions are derived which generate a set of pure shear basis vectors from any one member of the triad. The vector functions follow from compatibility condition for the pure shear basis vectors, and are independent of the principal stress values. The complementary types of vector basis have implications for the strain energy of linearly elastic solids with cubic material symmetry: for a given state of stress or strain, the strain energy achieves its extreme values when the material cube axes are aligned with principal axes of stress or with a pure shear basis. This implies that the optimal orientation for a given state of stress is with one or the other vector basis, depending as the stress is to be minimized or maximized, which involves the sign of one material parameter.

The algebraic proof of the fundamental theorem concerning pure shear, by making use only of the notion of orthogonal projector, is presented. It has been shown that the state of pure shear is the same for all singular symmetric traceless tensors in E3, up to the rotation.

As is known, electromechanical deformation of voltage-controlled dielectric elastomers (DEs) is significant but is susceptible to pull-in and snap-through instabilities, while the large stable deformation can be achieved by spraying charge on DE surfaces, i.e., charge-controlled DEs. In this article, we investigate the effect of constrained fibers on electromechanical actuation of charge-controlled DEs by involving two special deformation modes: uniaxial tension and pure shear state. The coupled effects between the geometrical sizes and the mechanical tensile force of the charge-controlled DEs are also explored. The research results indicate that, different from voltage-controlled DEs, the electromechanical stretch of charge-controlled DEs with constrained fibers does not always show a beneficial merit with respect to that of the charge-controlled DEs without constrained fibers.

A cantilever beam with elastic hinge pulled antagonistically by two dielectric elastomer (DE) membranes in tension forms a foldable actuator if one DE membrane is subject to a voltage and releases part of tension. Simply placing parallel rigid bars on the prestressed DE membranes results in enhanced actuators working in a pure shear state. We report design, analysis, fabrication, and experiment of soft mobile robots that are moved by such foldable DE actuators. We describe systematic measurement of the foldable actuators and perform theoretical analysis of such actuators based on minimization of total energy, and a good agreement is achieved between model prediction and measurement. We develop two versions of prototypes of soft mobile robots driven either by two sets of DE membranes or one DE membrane and elastic springs. We demonstrate locomotion of these soft mobile robots and highlight several key design parameters that influence locomotion of the robots. A 45 g soft robot driven by a cyclic triangle voltage with amplitude 7.4 kV demonstrates maximal stroke 160 mm or maximal rolling velocity 42 mm/s. The underlying mechanics and physics of foldable DE actuators can be leveraged to develop other soft machines for various applications.