A Generalized Framework and a Multiplicative Formulation of Electro-Mechanical Coupling
Electro-active polymers (EAP) recently attracted much interest because, upon electrical loading, EAP exhibit a large amount of deformation while sustaining large forces. On the other hand, generalized continuum frameworks are relevant to electro-mechanical coupled problems as they naturally incorporate couples or higher order stresses and can describe scale effects. Here, we want to adopt a strain gradient approach based on the generalized continuum framework as formulated in (Sansour in J. Phys. IV, Proc. 8:341–348, 1998; Sansour and Skatulla in Geomech. Geoeng. 2:3–15, 2007) and extend it to encompass the electro-mechanically coupled behavior of EAP. A new aspect of the electro-mechanical formulation relates to the multiplicative decomposition of the deformation gradient, well known from plasticity, into a purely elastic part and a further part which relates to the electric field. The formulation is elegant, makes for clarity and is numerically efficient. A numerical example of coupled large deformations is presented as well.
KeywordsDeformation Gradient Electric Displacement Move Least Square Multiplicative Decomposition Constitutive Tensor
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