Paper ID: 2409.13241 • Published Sep 20, 2024
Exploring energy minimization to model strain localization as a strong discontinuity using Physics Informed Neural Networks
Omar León, Víctor Rivera, Angel Vázquez-Patiño, Jacinto Ulloa, Esteban Samaniego
TL;DR
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We explore the possibilities of using energy minimization for the numerical
modeling of strain localization in solids as a sharp discontinuity in the
displacement field. For this purpose, we consider (regularized) strong
discontinuity kinematics in elastoplastic solids. The corresponding
mathematical model is discretized using Artificial Neural Networks (ANNs),
aiming to predict both the magnitude and location of the displacement jump from
energy minimization, i.e., within a variational setting. The
architecture takes care of the kinematics, while the loss function takes care
of the variational statement of the boundary value problem. The main idea
behind this approach is to solve both the equilibrium problem and the location
of the localization band by means of trainable parameters in the ANN. As a
proof of concept, we show through both 1D and 2D numerical examples that the
computational modeling of strain localization for elastoplastic solids using
energy minimization is feasible.