Complex interplay of nonlinear processes in dielectric elastomers

A combination of experiment and theory shows that dielectric elastomers exhibit complex interplay of nonlinear processes. Membranes of a dielectric elastomer are prepared in various states of prestretches by using rigid clamps and mechanical forces. Upon actuation by voltage, some membranes form wrinkles followed by snap-through instability, others form wrinkles without the snap-through instability, and still others fail by local instability without forming wrinkles. Membranes surviving these nonlinear processes are found to attain a constant dielectric strength, independent of the state of prestretches. Giant voltage-induced stretch of 3.6 is attained.

Figure 1

(a) In the reference state, under no force and voltage, the elastomer is of dimensions $L_1$, $L_2$, and $H$. (b) In the prestretched state, the elastomer is stretched horizontally, fixed to rigid clamps, and subjected to constant force $P$ in the vertical direction. The dimensions of the elastomer become ${\lambda }_{1p}{L}_1$, ${\lambda }_{2p}{L}_2$, and ${\lambda }_{3p}H$. (c) In the actuated state, subject to both the force $P$ and voltage Φ, the dimensions of the elastomer become ${\lambda }_1{L}_1$, ${\lambda }_2{L}_2$, and ${\lambda }_{3}H$. Photographs of an elastomer in (d) a prestretched state, (e) an actuated state at 2005 V, and (f) an actuated state at 2388 V. The faint horizontal lines in (d) and (e) are smear lines in the grease electrodes, which arise from the means of their application and have no influence on deformation of the elastomer.

Figure 2

The experimentally recorded voltage-stretch curves for clamped membranes prepared in various states of prestretches $\left\{{\lambda }_{1p},{\lambda }_{2p}\right\}$. Also included are voltage-stretch curves for unclamped membranes, marked by “U”.

Figure 3

Theoretical predictions of voltage-stretch curves for (a) unclamped elastomer subject to constant uniaxial forces, and (b)–(f) clamped elastomer subject to a constant vertical force. (b) Calculation assumes that ${\lambda }_2$ is fixed, and the open circles signify the loss of horizontal tension. (c)–(f) Before loss of tension, ${\lambda }_2$ is fixed by the clamps. After loss of horizontal tension, the elastomer is in effect unclamped.

Figure 4

The apparent electric breakdown fields for membranes prepared in various states of prestretches $\left\{{\lambda }_{1p},{\lambda }_{2p}\right\}$. The dots are experimental data. The lines correspond to intrinsic breakdown (B), loss of tension (T), stable states after the snap (S), and local instability (L).