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In this paper, a finite element model is used to describe the inhomogeneous deformations of dielectric elastomers (DE).
In our previous work, inhomogeneous deformations of the DE with simple boundary conditions represented by a system
of highly nonlinear coupled differential equations (ordinary and partial) were solved using numerical approaches [1-3].
To solve for the electromechanical response for complex shapes (asymmetric), nonuniform loading, and complex
boundary conditions a finite element scheme is required. This paper describes a finite element implementation of the DE
material model proposed in our previous work in a commercial FE code (ABAQUS 6.8-1, PAWTUCKET, R.I, USA).
The total stress is postulated as the summation of the elastic stress tensor and the Maxwell stress tensor, or more
generally the electrostatic stress tensor. The finite element model is verified by analytical solutions and experimental
results for planar membrane extensions subject to mechanical loads and an electric field: (i) equibiaxial extension and (ii)
generalized biaxial extension. Specifically, the analytical solutions for equibiaxial extension of the DE is obtained by
combining a modified large deformation membrane theory that accounts for the electromechanical coupling effect in
actuation commonly referred to as the Maxwell stress [4]. A Mooney-Rivlin strain energy function is employed to
describe the constitutive stress strain behavior of the DE. For the finite element implementation, the constitutive
relationships from our previously proposed mathematical model [4] are implemented into the finite element code.
Experimentally, a 250% equibiaxially prestretched DE sample is attached to a rigid joint frame and inhomogeneous
deformations of the reconfigurable DE are observed with respect to mechanical loads and an applied electric field. The
computational result for the reconfigurable DE is compared with the test result to validate the accuracy and robustness of
the finite element model. The active membrane is being investigated to simulate the deformation response of the
plagiopatagium of bat wing skins for a micro-aerial vehicle.
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