On the implementation of physical constraints for neural network modeling of hyperelastic materials at finite strains

With the rise of machine learning (ML) in recent decades, material modeling is one of the aspects of solid mechanics that has been the subject of applications of different ML techniques over the years. The most prominent of these ML techniques, with which this work also deals with, are neural networks (NNs). They have proven to be excellent candidates for modeling relations that are difficult to capture with conventional closed-form functions providing engineers with the ability to perform numerical analyses of more complex materials with greater confidence. However, NNs are often tools that are applied in a brute force manner without further thought given to their inner workings. In this work we give an overview of the possible restrictions that can be imposed on NNs via their construction and training in order to create an NN based material model which satisfies conditions usually imposed on material models in solid mechanics. This covers restrictions such as thermodynamic consistency, objectivity, normalization of energy and stress, non-negativity of strain energy, (poly)convexity and the growth condition. These topics are covered in the context of compressible and incompressible behavior with some results shown for models commonly used for modeling rubber-like materials.