DTE AICCOMAS 2025

Unsupervised Learning of Constitutive Model With Neural Networks and Sparse Identification of Internal Variables

  • Benady, Antoine (ETH Zurich)
  • Emmanuel, Baranger (Laboratoire mécanique Paris-Saclay)
  • Jailin, Clément (Laboratoire mécanique Paris-Saclay)
  • Chamoin, Ludovic (Laboratoire mécanique Paris-Saclay)

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Learning mechanical constitutive models using neural networks (NNs) is currently a widely researched topic. Representing thermodynamically consistent constitutive models with NNs is now a well-established approach, and such networks can be trained using measurable data within unsupervised frameworks, such as NN-EUCLID (see [1] for the original paper and [2] for an experimental validation) or NN-mCRE [3]. For history-dependent behavior [4], a current limitation in the unsupervised learning of complex constitutive models lies in the a priori selection of internal variables, rather than automatically discovering them during the training process. In [5], a supervised approach (relying on strain-stress data) is performed without prescribing internal variables, paving the way for unsupervised learning of constitutive models with automatic internal variable identification. The present work builds upon the NN-EUCLID framework and constitutes a preliminary study aimed at unsupervised learning of constitutive models represented by NNs without the need to predefine the structure of internal variables. The method is illustrated using synthetic digital image correlation data generated from a viscoelastic model. REFERENCES [1] P. Thakolkaran, A. Joshi, Y. Zheng, M. Flaschel, L. De Lorenzis, S. Kumar. NN-EUCLID: Deep-learning hyperelasticity without stress data. Journal of the Mechanics and Physics of Solids (2022). [2] C. Jailin, A. Benady, R. Legroux, E. Baranger. Experimental Learning of a Hyperelastic Behavior with a Physics-Augmented Neural Network. Experimental Mechanics (2024) [3] A. Benady, E. Baranger, L. Chamoin. NN-mCRE: A modified constitutive relation error framework for unsupervised learning of nonlinear state laws with physics-augmented neural networks. Int J Numer Methods Eng. (2024). [4] A. Benady, E. Baranger, L. Chamoin. Unsupervised learning of history-dependent constitutive material laws with thermodynamically-consistent neural networks in the modified Constitutive Relation Error framework. Computer Methods in Applied Mechanics and Engineering (2024) [5] Rosenkranz, M., Kalina, K.A., Brummund, J. et al. Viscoelasticty with physics-augmented neural networks: model formulation and training methods without prescribed internal variables. Comput Mech (2024).