144824 20250210083428.0 doi 10.1177/10812865241257850 sideral 139695 ART-2025-139695 eng Ayensa-Jiménez, Jacobo (orcid)0000-0003-2564-6038 Predicting and explaining nonlinear material response using deep physically guided neural networks with internal variables 2025 Access copy available to the general public Unrestricted Nonlinear materials are often difficult to model with classical state model theory because they have a complex and sometimes inaccurate physical and mathematical description, or we simply do not know how to describe such materials in terms of relations between external and internal variables. In many disciplines, neural network methods have emerged as powerful tools to identify very complex and nonlinear correlations. In this work, we use the very recently developed concept of physically guided neural networks with internal variables (PGNNIVs) to discover constitutive laws using a model-free approach and training solely with measured force–displacement data. PGNNIVs make a particular use of the physics of the problem to enforce constraints on specific hidden layers and are able to make predictions without internal variable data. We demonstrate that PGNNIVs are capable of predicting both internal and external variables under unseen loading scenarios, regardless of the nature of the material considered (linear, with hardening or softening behavior and hyperelastic), unravelling the constitutive law of the material hence explaining its nature altogether, endowing the method with some explanatory character that distances it from the traditional black box approach. info:eu-repo/semantics/closedAccess All rights reserved http://www.europeana.eu/rights/rr-f/ info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Orera-Echeverría, Javier Universidad de Zaragoza Doblare, Manuel Universidad de Zaragoza (orcid)0000-0001-8741-6452 5008 800 Universidad de Zaragoza Dpto. Ingeniería Electrón.Com. Área Teoría Señal y Comunicac. 5004 605 Universidad de Zaragoza Dpto. Ingeniería Mecánica Área Mec.Med.Cont. y Teor.Est. 30, 2 (2025), 573-598 Math. mech. solids MATHEMATICS AND MECHANICS OF SOLIDS 1081-2865 1940338 http://zaguan.unizar.es/record/144824/files/texto_completo.pdf Versión publicada 1774085 http://zaguan.unizar.es/record/144824/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:144824 articulos driver 2025-02-10-08:31:25 ARTICLE