Convex Neural Networks for Material Behavior Modeling

This technical report presents a novel machine learning framework called Generalized Standard Material Networks, which utilizes convex neural networks to learn the mechanical behavior of generalized standard materials. The framework is based on the theory that two thermodynamic potentials, namely the Helmholtz free energy density and the dissipation rate density potential, govern the constitutive material response while ensuring thermodynamic consistency. The authors detail the architecture of the neural networks used to parameterize these potentials and describe how automatic differentiation, an implicit time integration scheme, and the Newton-Raphson method are employed to capture various material behaviors, including elastic, viscoelastic, plastic, and viscoplastic responses. The report discusses the framework's performance on synthetic data generated by benchmark material models, highlighting its prediction accuracy and robustness to noise. Additionally, the authors address the non-uniqueness of thermodynamic potentials and the balance between fitting accuracy and model complexity through the selection of internal variables.