Utilizing physics‐augmented neural networks to predict the material behavior according to Yeoh's law

• Published in: Proceedings in applied mathematics and mechanics Vol. 24; no. 4
• Main Authors: Maurer, Lukas, Eisenträger, Sascha, Kalina, Karl, Juhre, Daniel
• Format: Journal Article
• Language: English
• Published: 01.12.2024
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.202400213

This article discusses physics‐augmented neural network approaches in the field of hyperelastic material modeling. Physical conditions such as objectivity, material symmetry, or a stress– and energy‐free reference configuration are considered in the construction of the neural networks. In addition, a new approach for stress normalization is proposed. The neural network is used to learn the behavior of Yeoh's constitutive model with sparse data. Finally, the trained networks are incorporated into a three‐dimensional finite element framework and compared with the classical material model in terms of accuracy. The paper demonstrates the ability of physics‐augmented neural networks to model hyperelastic materials using a small amount of data that could be generated by experiments. Compared to the classical constitutive laws of Yeoh's model, our trained material showed no material instabilities that could occur due to poorly chosen material parameters.