Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks
This work addresses contact mechanics problems in engineering, but it is incremental as it applies existing PINN methods with enhancements to a specific domain.
The paper tackled forward and inverse problems in contact mechanics for small deformation elasticity using physics-informed neural networks (PINNs), showing that PINNs can serve as a PDE solver, data-enhanced model, inverse solver, and surrogate model with improved accuracy and training time through optimized hyperparameters and optimizers.
This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output transformation to enforce Dirichlet and Neumann boundary conditions as hard constraints. Inequality constraints of contact problems, namely Karush-Kuhn-Tucker (KKT) type conditions, are enforced as soft constraints by incorporating them into the loss function during network training. To formulate the loss function contribution of KKT constraints, existing approaches applied to elastoplasticity problems are investigated and we explore a nonlinear complementarity problem (NCP) function, namely Fischer-Burmeister, which possesses advantageous characteristics in terms of optimization. Based on the Hertzian contact problem, we show that PINNs can serve as pure partial differential equation (PDE) solver, as data-enhanced forward model, as inverse solver for parameter identification, and as fast-to-evaluate surrogate model. Furthermore, we demonstrate the importance of choosing proper hyperparameters, e.g. loss weights, and a combination of Adam and L-BFGS-B optimizers aiming for better results in terms of accuracy and training time.