Electromechanics

Material structure and total stress in the field presence Stress tensor in electric field - Dielectrostriction
- Electro-elasticity and birefringence

Dielectrostriction

- Fundamental property of any material
- Modelling: New electroactive materials
- Detection: New sensing approaches

Dielectrostriction sensor: Contactless detection

- Strains/stresses
- Contactless/non-destruction detection of fiber orientation
- Tactile sensors

Fatigue

Field-Aided Manufacturing (FAiMTA)

Stress tensor in electric field

Constitutive equation for stress tensor, σ_{ik}, has term linear with strain, u_{lm}, as in Hooke's Law

σ_{ik}=λ_{iklm}u_{lm}.

This relation is corrected on additional contribution due to columbic attraction between field induced charges λ^{E}_{iklm }u_{lm}.

Additional contribution due to realignment material structure due to polarization is described through derivatives of the dielectric tensor ε_{lm}:

-ε_{0}/2 ∂ε_{lm}/∂u_{ik }E_{l} E_{m}.

For more details see:

*Yuri M Shkel, “Electrostriction: material parameters and stress/strain constitutive relations,” Philosophical Magazine, 2007*.

Dielectrostriction

Constitutive equation for dielectric tensor in isotropic materials, ε_{ik}, has a term linear with strain, u_{ik}, as in Figure (a), and a term linear with volume deformations as in Figure (b).

Two material parameters, α_{1 }and α_{2}, determine dielectric tensor in isotropic materials.

In figure these two parameters are calculated based on a model of polarizable inclusions under affine deformations. For more details see reference:

*Y. M. Shkel and D. J. Klingenberg, “Electrostriction of Polarizable Materials…,” J. Appl. Phys., 83, (1998). *

Electrostriction Driven Beam

A block of silicone rubber is attached to interdigitated electrodes. AC voltage periodically vary effective rigidity of the rubber which is described by function

γ(t) in the dynamic equation on the image. Function

h(t) describes possible external forces. Beam vibrates with double frequency of the applied voltage. A

video file shows voltage frequency scan near resonance frequency of the beam:

Dielectrostriction

Constitutive equation for dielectric tensor in isotropic materials, ε_{ik}, has a term linear with strain, u_{ik}, as in Figure (a), and a term linear with volume deformations as in Figure (b).

Two material parameters, α_{1 }and α_{2}, determine dielectric tensor in isotropic materials.

In figure these two parameters are calculated based on a model of polarizable inclusions under affine deformations. For more details see reference:

*Y. M. Shkel and D. J. Klingenberg, “Electrostriction of Polarizable Materials…,” J. Appl. Phys., 83, (1998). *

Fatigue

Feasibility of dielectrostriction for detection of material fatigue has been demonstrated by following test:

A 5" specimen is loaded by shaker with Amplitude 0.6 mm and frequency 30 Hz. Voltage output is recorded for range of 10^{2} ~ 2×10^{6 }cycles.