Dielectric elastomers, widely used as smart materials in soft actuators [1], face significant challenges that limit their performance. Fiber-reinforced dielectric elastomers, with their anisotropic behavior, offer enhanced mechanical properties, such as faster response rates under electric fields [2]. While many studies incorporate hyperelasticity and anisotropy, time-dependent viscoelastic effects are often included to improve material models. Classical viscoelastic models can describe these effects accurately in specific cases, but fractional viscoelasticity offers a more powerful alternative. By assuming a power-law relaxation spectrum, fractional viscoelasticity reduces the number of required parameters while effectively capturing a continuous distribution of timescales [3]. This study presents a unified framework for modeling the coupled nonlinear electro-mechanical behavior of fiber-reinforced anisotropic dielectric elastomers with fractional viscoelastic effects. The approach builds on an anisotropic hyperelastic nearly-incompressible model and employs a multiplicative decomposition of the deformation gradient, incorporating fractional viscoelasticity to model time-dependent mechanical responses with minimal number of additional parameters. The weak form is derived for efficient numerical implementation using the open-source finite element platform FEniCSx. Validation through dynamic deformation simulations, including electro-mechanical instability and bending, demonstrates the favorable influence of anisotropy on actuation performance, the capability of fractional viscoelasticity to capture complex time-dependent behavior, and the computational efficiency of the developed framework. This work provides a foundation for future extensions to thermal and magnetic couplings, advancing the modeling of soft active materials.

[1] Tewary, M., & Roy, T. (2023). Nonlinear dynamic analysis of anisotropic bimorph dielectric elastomer actuator for soft fish robots. Communications in Nonlinear Science and Numerical Simulation, 127, 107585.

[2] Hossain, M., & Steinmann, P. (2018). Modelling electro-active polymers with a dispersion-type anisotropy. Smart Materials and Structures, 27(2), 025010.

[3] Zhang, W., Capilnasiu, A., Sommer, G., Holzapfel, G. A., & Nordsletten, D. A. (2020). An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials. Computer methods in applied mechanics and engineering, 362, 112834.