Robust Calibration of Constitutive Models from Full-Field Data Using Data-Driven Identification and Neural Networks
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The formulation and calibration of constitutive models for materials exhibiting complex nonlinear behavior remain challenging tasks in computational mechanics. In recent years, data-driven approaches have gained increasing attention; however, they typically rely on extensive datasets containing stress–strain information [1, 2]. In this contribution, we present a robust dual-stage framework for the automated calibration of hyperelastic constitutive models that is based solely on experimentally accessible quantities. In the first step, data-driven identification (DDI) is employed to extract stress–strain pairs from prescribed boundary conditions and displacement fields, which can be obtained using full-field measurement techniques such as digital image correlation (DIC) [2]. In the second step, the identified data are used to calibrate a physics-augmented neural network (PANN) [3]. By construction, the PANN satisfies the fundamental principles of hyperelasticity while retaining a high degree of flexibility and enabling straightforward integration into finite element (FE) simulations. The proposed framework is demonstrated using several representative numerical examples. To this end, synthetic two-dimensional datasets generated from reference constitutive models are employed in the data-driven identification step to extract stress–strain information, which serves as training data for the PANN. In addition, the influence of noisy input data and loading scenarios on the identified material response is discussed, highlighting the robustness of the proposed methodology and its practical relevance. [1] A. Leygue, M. Coret, J. Réthoré, L. Stainier, E. Verron, Data-based derivation of material response, Computer Methods in Applied Mechanics and Engineering 331 (2018). [2] L. Linden, K. A. Kalina, J. Brummund, B. Riemer, M. Kästner, A dual-stage constitutive modeling framework based on finite strain data-driven identification and physics-augmented neural networks, Computer Methods in Applied Mechanics and Engineering 447 (2025). [3] L. Linden, D. K. Klein, K. A. Kalina, J. Brummund, O. Weeger, M. Kästner, Neural networks meet hyperelasticity: A guide to enforcing physics, Journal of the Mechanics and Physics of Solids 179 (2023).
