Design Principles

Basic Theory

The theory behind dielectric elastomer actuators is the same as that of a fundamental circuit element: the capacitor. Below is a simple (likely familiar!) diagram of a parallel-plate capacitor.

When voltage is applied onto a capacitor, charges will flow in the direction of the voltage - positive to negative, and vice versa. However, the separation between capacitor electrodes prevents the charges from flowing freely, causing the accumulation of positive charges on one end, and negative charges on another.

Opposite charges attract, and an electric field is formed as the accumulated negative and positive charges attempt to meet one another. The physical separation between them prevents this from occurring, but a force is still generated by the presence of the electric field.

DEA's take advantage of this force by sandwiching an elastic material, known as a dielectric, in between the electrodes. The attractive force squeezes the dielectric, creating a change in shape that can be taken advantage of. As pictured below, it becomes thinner in the axis normal to the electrodes, and widens in the plane parallel to the electrodes.

Grey arrows indicate the directions in which stretching and contraction occurs. Note that these are applied to both the electrodes and the dielectric.

DEA's use flexible electrodes, because the dielectric cannot change shape if it is attached to a rigid, inflexible plate. If you are familiar with capacitors, you may recall that their properties are related to their geometry (including the area of the two plates, and thickness between them). Thus, if the electrodes themselves are changing shape, mathematically representing this system might initially seem like a daunting task!

However, we can still create a model to represent this system by using values that are independent of the area of our capacitor electrodes. For real-world applications, we will need to model the relationship between the applied voltage, and the change in thickness of the dielectric.

This relationship is rather easy to derive (which you can investigate by opening the "Derivation" box below).

Derivation

We start by considering the relationship between stress and strain:

S = TxY

where: S is the strain (change in dielectric thickness, divided by the original thickness)

T is the stress (force between electrodes, divided by area)

Y is the Young's modulus (a material-specific constant that relates the above two values)

Since we can easily derive the change in thickness from the strain S, we simply need a way to relate S to an applied voltage. The electric field E between the electrodes of a capacitor is given by:

E = V/D

where: V is the voltage between electrodes

D is the distance between the electrodes

We combine this with the equation for the Maxwell stress (a term for the stress applied by electromagnetic fields -- which can get quite complex, but here, we keep things simple by assuming the net stress T is the Maxwell stress):

T = (KxZ) x (E^2)

where: K is the dielectric's dielectric constant (another material-specific constant, representing how easily an electric field propagates through the material)

Z is the permittivity of free space (a constant equal to 8.854 x 10^-12 Farad/meter)

Combining our three expressions together, we can derive the relation between S and V stated below.

Design Considerations

In designing your own DEA, there are a couple of points to consider. At worst, these will greatly improve the performance of your actuator, and at best, you'll avoid total failure of the actuator altogether.

For further reading, you may also refer to Soft Robotics Toolkit and their section on DEA's, containing more details on design considerations and testing.

Prestretching

Dielectric elastomers used in DEA's are usually sheet silicone or acrylic tape that is manufactured to a preset thickness, typically ranging from 0.1 mm to 2.0 mm. This is actually not thin enough to see reliable actuation in a DEA, and one way to get a thinner dielectric is to stretch it prior to applying voltage; hence, prestretching. Prestretching is done by stretching the dielectric material and attaching it to an external, rigid frame (see: Fabrication).

Dielectric Breakdown

Dielectric breakdown is a mode of failure that occurs if the dielectric is too thin, or the voltage too high. The electric field generated in a capacitor is sustained because of the physical separation of electric charge. But similar to an overstretched rubber band, if the voltage becomes too high, or the separation between charges too thin, the separated charges will suddenly "jump" between the capacitor electrodes, causing a discharge and likely burning a hole through your dielectric!

As a side note, this phenomena is actually the same reason lightning can split the skies, or a bit of static can arc between you and a . Air can act as a dielectric, and despite its reputation as a strong insulator, a high enough voltage or low enough separation distance will permit electric charges to travel through air! The result can range from being a minor annoyance, to the awe-inspiring power of a thunderstorm.

References

R. Pelrine, R. Kornbluh, Q. Pei, and J. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science, vol. 287, pp. 836-839, 2000.

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