Speaker
Description
Ferroelectric as well as ferromagnetic materials are widely used in smart structures and devices as actuators, sensors etc. Regarding their nonlinear behavior, a variety of models has been established in the past decades. Investigating hysteresis loops or electromechanical/magnetoelectric coupling effects, only simple boundary value problems (BVP) are considered. In [1] a new scale–bridging approach is introduced to investigate the polycrystalline ferroelectric behavior at a macroscopic material point (MMP) without any kind of discretization scheme, the so-called Condensed Method (CM). Besides classical ferroelectrics, other fields of application of the CM have been exploited, e.g. [2, 3, 5]. Since just the behavior at a MMP is represented by the CM, the method itself is unable to solve complex BVP, which is technically disadvantageous if a structure with e.g. notches or cracks shall be investigated. In this paper, a concept is presented, which integrates the CM into a Finite Element (FE) environment [4]. Considering the constitutive equations of a homogenized MMP in the weak formulation, the FE framework represents the polycrystalline behavior of the whole discretized structure, which finally enables the CM to handle arbitrary BVP. A more sophisticated approach, providing a basis for a model order reduction, completely decouples the constitutive structure from the FE discretization by introducing an independent material grid. Numerical examples are finally presented in order to verify the approach.
References
[1] Lange, S. and Ricoeur, A., A condensed microelectromechanical approach for modeling tetragonal ferroelectrics,International Journal of Solids and Structures 54, 2015, pp. 100 – 110.
[2] Lange, S. and Ricoeur, A., High cycle fatigue damage and life time prediction for tetragonal ferroelectricsunder electromechanical loading, International Journal of Solids and Structures 80, 2016, pp. 181 – 192.
[3] Ricoeur, A. and Lange, S., Constitutive modeling of polycrystalline and multiphase ferroic materials basedon a condensed approach, Archive of Applied Mechanics 89, 2019, pp. 973 – 994.
[4] Wakili, R., Lange, S. and Ricoeur, A., FEM-CM as a hybrid approach for multiscale modeling and simulationof ferroelectric boundary value problems, Computational Mechanics 72, 2023, pp. 1295 – 1313.
[5] Warkentin, A. and Ricoeur, A., A semi-analytical scale bridging approach towards polycrystalline ferroelectricswith mutual nonlinear caloric–electromechanical couplings, International Journal of Solids andStructures 200 – 201, 2020, pp. 286 – 296.
