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<p>In elastohydrodynamic lubrication (EHL) simulations, classical numerical methods like the finite difference method (FDM) and the finite element method (FEM) are commonly employed. While PINNs have proven to be a suitable alternative for fluid simulation, this work focuses on approximating the deformation of the hyperelastic counterbody using physics-informed machine learning (PIML) and comparing the results with FEM reference solutions. In this paper, nonlinear deformation is calculated using the deep energy method (DEM), leveraging both physics-informed neural networks (PINNs) and physics-informed graph neural networks (PI-GNNs) to approximate the displacement field. The novelty of this work lies in the implementation of an advanced hyperelasticity framework, employing Bayesian optimization to determine optimal hyperparameters. A comparison of results obtained from PINN and PI-GNN shows that both approaches achieve a high level of accuracy in predicting hyperelastic deformation.</p>

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Advancing deformation calculation: a physics-informed deep graph learning framework for hyperelastic materials

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月22日

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  • Faras Brumand-Poor,
  • Matthias Trautmann,
  • Katharina Schmitz

摘要

In elastohydrodynamic lubrication (EHL) simulations, classical numerical methods like the finite difference method (FDM) and the finite element method (FEM) are commonly employed. While PINNs have proven to be a suitable alternative for fluid simulation, this work focuses on approximating the deformation of the hyperelastic counterbody using physics-informed machine learning (PIML) and comparing the results with FEM reference solutions. In this paper, nonlinear deformation is calculated using the deep energy method (DEM), leveraging both physics-informed neural networks (PINNs) and physics-informed graph neural networks (PI-GNNs) to approximate the displacement field. The novelty of this work lies in the implementation of an advanced hyperelasticity framework, employing Bayesian optimization to determine optimal hyperparameters. A comparison of results obtained from PINN and PI-GNN shows that both approaches achieve a high level of accuracy in predicting hyperelastic deformation.