Modelización de mecanismos de falla dúctiles en barras utilizando redes neuronales artificiales

Abstract

This research work focuses on modeling mechanisms of ductile failure in a one-dimensional bar. The main objective is to use methods based on Physics-Informed Neural Networks (PINN) and Machine Learning, employing the variational approach, to model the mechanism of ductile failure and deformation localization. Two implementations of PINN have been developed based on the variational principle, using different energy minimization equations that are equivalent to each other. The obtained results demonstrate that neural networks are capable of capturing elastoplastic behavior without the need for complex tools such as phase-fields. This numerical approach presents a promising option compared to alternative methods like finite elements, particularly for problems in higher dimensions where other methods show limitations. This opens up new lines of research in the field of modeling failure mechanisms in solids. It has been shown that these neural networks, applied through the variational principle, offer sufficient accuracy compared to analytical solutions. As a recommendation, it is suggested to further explore the nature of neural networks as a method for problem-solving in solid mechanics, as well as to implement neural networks in solving problems in 2D and 3D, which represents a future line of research.