A dielectric elastomer actuator (DEA) is a soft rubber film sandwiched between two compliant electrodes. Applying voltage V across the thickness t creates a field E = V / t. Opposite charges on the two electrodes attract, generating a compressive electrostatic (Maxwell) pressure on the film:
E = V / t
p = ε₀ εᵣ E² (Maxwell stress, ε₀ = 8.854×10⁻¹² F/m)
The film resists with its elastic modulus Y. For small strain the net compressive pressure (Maxwell stress minus any external bias load) produces a thickness strain, and — because rubber is nearly incompressible (Poisson's ratio ≈ 0.5) — that lost thickness has to go somewhere, so the film bulges outward in area:
s_z = max(0, p − p_bias) / Y (thickness compression)
t = t₀ (1 − s_z)
r/r₀ = (1 − s_z)^(−1/2) (incompressible volume)
- Material — swaps permittivity εᵣ and elastic modulus Y between three real actuator materials.
- Voltage — the drive signal; pressure grows with the square of the field, so actuation is highly nonlinear.
- Film thickness — thinner films reach the same field E at lower voltage, but are more fragile.
- Bias load — an external mechanical load (e.g. a spring or payload) that the actuator has to overcome before it can expand.
This 2D version renders the true cross-section: film thickness compressing, radial bulge, surface charge density on the electrodes, and a live strain-vs-voltage curve traced against the material's dielectric breakdown limit.