Dielectric elastomers undergo large deformations in response to an electric field and consequently have attracted significant interest as electromechanical transducers. Applications of these materials include actuators capable of converting an applied electric field into mechanical motion and energy harvesting devices that convert mechanical energy into electrical energy. Numerically-based design tools are needed to facilitate the development and optimization of these devices.

A design capability for dielectric elastomers requires (i) a finite-deformation constitutive theory for the electromechanically-coupled response of these materials and (ii) a robust numerical implementation of the resulting field equations.  Work on electromechanically-coupled constitutive theories goes back many decades, and in recent years the mechanics community has come to a relative agreement regarding the formulation of a theory in a thermodynamic framework.  However, there remains a need for numerical tools capable of predicting the large-deformation, three-dimensional, coupled response.  Several approaches have been undertaken.  First, simplified finite-element computational procedures have been proposed that make geometrical assumptions, reducing the electrical problem to one dimension.  These techniques are useful for basic actuator configurations; however, fully three-dimensional procedures are needed to guide the design of more complex devices.  Recently, finite-element implementations have been reported using in-house codes both in quasi-static and dynamic settings; however, these codes are not available to the community. Given the industrial and scientific community's growing interest in dielectric elastomers, implementation of the theory within a widely-available finite-element software is a crucial step toward facilitating interactions between industry and researchers and guiding the design of complex three-dimensional devices. Unfortunately, this task is not straightforward within commercial finite-element packages, since additional nodal degrees of freedom are required.  Few efforts in this direction have been reported, namely using  FEAP  and Comsol. However, since FEAP is a general-purpose finite-element program, designed for research and educational use, it is not available to the industrial community. Moreover, although Comsol is amenable to the implementation of the coupled electromechanical theory, its difficulty in dealing with large deformations is well-known, and as such, it is not well-suited for problems involving dielectric elastomers.

To overcome these issues, we recently  implemented the theory  in the commercial finite-element code Abaqus, taking full advantage of the capability to actively interact with the software through user-defined subroutines, and  utilized the code to provide new insights, through simulation, into the design and optimization of complex actuators and energy harvesting devices in various settings.  Abaqus is an attractive platform because it is a well-known code, widely-available, stable, portable, and particularly suitable for analyses involving large deformations.    We expect our simulations of actuators and energy harvesting devices to aid in improving upon the designs of these structures.  Further, our Abaqus user-defined subroutines and input files may be found online as supplementary material to be used and expanded upon by the community in further research on dielectric elastomers.

Furthermore, recently we started investigating instabilities in composite structures made of dielectric elastomers.  Experimental observations clearly show that the performance of dielectric elastomeric-based devices can be considerably improved using composite materials. A critical issue in the development of composite dielectric materials toward applications is the prediction of their failure mechanisms due to the applied electromechanical loads. We  investigated  analytically the influence of electromechanical finite deformations on the stability of multilayered soft dielectrics under plane-strain conditions. Four different criteria are considered: i.) loss of positive definiteness of the tangent electroelastic constitutive operator, ii.) existence of diffuse modes of bifurcation ( microscopic modes), iii.) loss of strong ellipticity of the homogenized continuum (localized or macroscopic modes), and iv.) electric breakdown.

Using our  simulation capability we are currently investigating  the non-linear response of complex dielectric structures and devices in various settings.

Publications:

• K. Bertoldi and M. Gei. Instabilities in multilayered soft dielectrics. Journal of the Mechanics and Physics of Solids, 59: 18-42, 2011.
• D.L. Henann, S.A. Chester and K. Bertoldi. Modeling of dielectric elastomers: design of actuators and energy harvesting devices. Journal of the Mechanics and Physics of Solids, 2013