Convex neural networks learn generalized standard material models

Abstract

We propose Generalized Standard Material Networks, a machine learning framework based on convex neural networks for learning the mechanical behavior of generalized standard materials. The theory of these materials postulates the existence of two thermodynamic potentials, the Helmholtz free energy density and the dissipation rate density potential, which alone determine the constitutive material response with guaranteed thermodynamic consistency. We parameterize the two potentials with two artificial neural networks and, due to a specifically designed network architecture, we satisfy by construction all the needed properties of the two potentials. Using automatic differentiation, an implicit time integration scheme and the Newton-Raphson method, we can thus describe a multitude of different material behaviors within a single unified overarching framework, including elastic, viscoelastic, plastic, and viscoplastic material responses with hardening. By probing our framework on the synthetic data generated by five benchmark material models, we demonstrate satisfactory prediction accuracy to unseen data and a high robustness to noise. In this context, we observe a non-uniqueness of thermodynamic potentials and discuss how this affects the results of the training process. Finally, we show that a carefully chosen number of internal variables strikes a balance between fitting accuracy and model complexity.