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

Advanced Modeling and Simulation in Engineering Sciences, vol. 12

Abstract

Abstract 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.

Authors 3

1. Faras Brumand‐Poor corresponding Aachen Institute for Fluid Power Drives and Systems

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute for Fluid Power Drives and Systems (ifas), Campus-Boulevard 30, 52074, Aachen, Germany

2. Matthias Trautmann Aachen Institute for Fluid Power Drives and Systems

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute for Fluid Power Drives and Systems (ifas), Campus-Boulevard 30, 52074, Aachen, Germany

3. Katharina Schmitz Aachen Institute for Fluid Power Drives and Systems

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute for Fluid Power Drives and Systems (ifas), Campus-Boulevard 30, 52074, Aachen, Germany