COMPLAS 2023

Modeling Elastoplastic Constitutive Behavior Using Physics-Informed Neural Networks

  • Santos, Luis (Tecgraf Institute/PUC-Rio)
  • Mejia, Cristian (Tecgraf Institute/PUC-Rio)
  • Roehl, Deane (Tecgraf Institute/PUC-Rio)

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Conventional modeling of elastoplastic material response is often challenging due to the nonlinear material behavior. The most common problem associated with modeling is the high computational cost, especially in large-scale simulations. Recently, deep learning models have been employed as a robust methodology capable of learning patterns and simulating these complex mechanisms [1]. One of the most recent research topics in the deep learning field is physically informed neural networks (PINNs), which adds physical and theoretical knowledge as constraints to the training process. Compared to deep neural networks (DNN), PINNs often have a high generalization capability with lower demand for training data. Also, no mesh generation is demanded. This work presents the application of PINNs to modeling the nonlinear elastoplastic response of mechanical materials, emphasizing its ability to provide accurate results. The best neural network architecture is obtained through a sensitivity study of each hyperparameter (i.g. the number of hidden layers, neurons per layer). A hyperbolic tangent activation function is adopted for all hidden layers. To minimize the loss function, Adam, followed by the L-BFGS algorithm, is considered, as presented in recent developments [2]. We demonstrate that the output of the trained network is in excellent agreement with the results obtained from nonlinear finite element analysis, validating its accuracy and effectiveness. Finally, the outstanding results demonstrate the computational efficiency of physics-informed neural networks in forecasting the nonlinear response of materials. [1] Haghighat, E., Raissi, M., Moure, A., Gomez, H. and Juanes, R., 2021. A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. Computer Methods in Applied Mechanics and Engineering, 379, p.113741. [2] L. Lu, X. Meng, Z. Mao, e G. E. Karniadakis, “DeepXDE: A deep learning library for solving differential equations”, SIAM Review, vol. 63, no 1, p. 208–228, 2021, doi: 10.1137/19M1274067.