Multiscale analysis of the electromechanical coupling in dielectric elastomers. (English) Zbl 1406.74212
Summary: The coupled electromechanical response of dielectrics is analyzed in terms of the local response and the distribution of its microstructural unit elements. A comparison between two variational statements for a continuous and a discrete systems results in an estimate for the macroscopic coupled electromechanical energy-density function. Next, a few types of unit elements are considered and the corresponding behaviors of dielectrics with a random distribution of these elements are calculated. Additionally, to highlight the possible effect of local constraints among the unit elements, a deterministic model for a network of polymer chains is proposed and its response to electric excitation is determined. The practically common case of a uniaxial stretch aligned with the electric field is examined in detail and the results are compared with widely accepted macroscopic models and available experimental results.
MSC:
| 74F15 | Electromagnetic effects in solid mechanics |
| 74B20 | Nonlinear elasticity |
| 78A48 | Composite media; random media in optics and electromagnetic theory |
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