Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variables
This work addresses the challenge of accurately modeling complex nonlinear materials in fields like materials science and engineering, offering an explainable AI approach, though it appears incremental as it builds on recent PGNNIV concepts.
The authors tackled the problem of modeling nonlinear materials by using Physically Guided Neural Networks with Internal Variables (PGNNIV) to discover constitutive laws from force-displacement data, demonstrating that PGNNIVs can predict internal and external variables for various material types without needing internal variable data.
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 arisen as powerful tools to identify very complex and non-linear correlations. In this work, we use the very recently developed concept of Physically Guided Neural Networks with Internal Variables (PGNNIV) 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 load 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, placing the method in what is known as eXplainable Artificial Intelligence (XAI).