A Finite Element Framework for Geometrically Nonlinear Hyperelastic Piezoelectrics

  • Seibert, Jakob (FAU Erlangen-Nürnberg)
  • Mergheim, Julia (FAU Erlangen-Nürnberg)

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Flexible piezoelectric materials such as polyvinylidene fluoride (PVDF) have attracted increasing interest in recent years [1]. Due to their high strain tolerance, they are well suited for energy harvesting applications such as implants or wearable devices. However, most piezoelectric constitutive models are formulated with linearized kinematics and are therefore limited to small strains. While such models are sufficient for materials like lead zirconate titanite (PZT), they are not suitable for PVDF-based devices operating under large deformations. In this work, a continuum-based formulation for geometrically nonlinear hyperelastic piezoelectric materials is presented. The model is derived from an energy-based framework combining the Neo-Hookean material model and electromechanical theory in a total Lagrangian setting. The resulting mechanically dynamic and electrostatic field equations are solved monolithically using the finite element method. This enables computation of spatially resolved electromechanical quantities under dynamic loading, enhancing reduced-order hybrid [2] and quasi-static [3] modeling approaches. Furthermore, this approach allows coupling to external circuits. The proposed framework is illustrated through numerical simulations for selected configurations. These demonstrate its applicability to large strain piezoelectric problems. REFERENCES [1] Concha, V.O.C., Timóteo, L., Duarte, L.A.N. et al., Properties, characterization and biomedical applications of polyvinylidene fluoride (PVDF): a review, J Mater Sci, 59, 14185–14204, (2024). https://doi.org/10.1007/s10853-024-10046-32024. [2] Maruccio C., Quaranta, G., Montegiglio, P., Trentadue, F., Acciani, G., A Two-Step Hybrid Approach for Modeling the Nonlinear Dynamic Response of Piezoelectric Energy Harvesters, Shock and Vibration, 2054873, (2018). https://doi.org/10.1155/2018/2054873. [3] Lv, S., Meng, L., Zhang, Q., Shi, Y., Gao, C., Numerical framework for anisotropic flexible piezoelectrics with large deformation, International Journal of Mechanical Sciences, 258, 108564, (2023). https://doi.org/10.1016/j.ijmecsci.2023.108564.