Data-Driven Modeling of Nonlinear Ferroelectric Behavior Using Micromechanics-Based Multiscale Models with Internal Variables
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Ferroelectric materials exhibit strongly nonlinear and history-dependent behavior governed by complex multiscale mechanisms such as domain switching, internal dissipation, and path-dependent evolution of internal state variables. Micromechanics-based multiscale models with internal variables provide a physically well-founded framework to capture these effects, but their direct numerical evaluation remains computationally expensive, particularly in large-scale or transient simulations. In this contribution, we propose a data-driven modeling approach in which neural networks are trained on data generated from micromechanics-based multiscale models with internal variables describing the macroscopic behavior of ferroelectrics. Owing to the intrinsic history dependence of the underlying constitutive behavior, the learning task is formulated within a recurrent framework. We investigate recurrent neural network (RNN) architectures, with a primary focus on Long Short-Term Memory (LSTM) networks, and compare them to alternative approaches such as multi-layer perceptrons (MLPs) equipped with explicit feedback of internal state information. In addition, the potential of transformer-based architectures for constitutive modeling of ferroelectric materials is discussed. The resulting neural networks serve as surrogate representations of the history-dependent multiscale constitutive behavior. The approach demonstrates the potential for computationally more efficient evaluations and for interpolative use across selected loading histories and material parameter ranges without repeated multiscale simulations. Furthermore, the framework provides a flexible setting for combining simulation data, experimental measurements, and physics-enhanced constraints, indicating a viable pathway toward hybrid data-driven and physics-augmented constitutive modeling of ferroelectric materials
