In the last decades, a vast amount of highly specialized metamaterials has been developed and, with advancing requirements in engineering applications, the trend is growing. Often comprised of complex multiphysical microstructures, these materials can be tailored for each specific application. At the same time, this sets a challenge for the mechanical description of such materials, as they behave highly nonlinear. Thus, we envision the use of physics-augmented neural networks (PANNs), circumventing the current limitations of analytically formulated material models. In [1], a PANN constitutive model for electro-mechanically coupled material behavior at finite deformations was proposed. Using electro-mechanically coupled invariants as inputs for convex neural networks, a polyconvex internal energy is constructed. In this way, the model fulfills common constitutive conditions such as objectivity and ellipticity by construction. In the present work [2], the applicability of the PANN constitutive model for complex electro-elastic finite element analysis (FEA) is demonstrated. For this, boundary value problems inspired by engineering applications of composite electro-elastic materials are considered. Including large electrically induced deformations and instabilities, such scenarios are particularly challenging, and thus necessitate extensive investigations of the PANN constitutive model. First of all, an excellent prediction quality of the model is required for very general load cases occurring in the simulation. Furthermore, simulation of large deformations and instabilities poses challenges on the stability of the numerical solver, which is closely related to the constitutive model. For the investigations, PANN models are calibrated to different synthetically generated datasets. In all cases, the PANN models yield excellent prediction qualities and a stable numerical behavior. Lastly, the models are calibrated to experimental data of electro-active polymers. [1] D. K. Klein, R. Ortigosa, J. Martínez-Frutos, O. Weeger. Finite electro-elasticity with physics-augmented neural networks. CMAME 400:115501 (2022). [2] D. K. Klein, R. Ortigosa, J. Martínez-Frutos, O. Weeger. Nonlinear electro-elastic finite element analysis with neural network constitutive models. In preparation.