A neural ordinary differential equation framework for modeling inelastic stress response via internal state variables

Abstract: We propose a neural network framework to preclude the need to define or observe incompletely or inaccurately defined states of a material in order to describe its response. The neural network design is based on the classical Coleman-Gurtin internal state variable theory. In the proposed framework the states of the material are inferred from observable deformation and stress. A neural network describes the flow of internal states and another represents the map from internal state and strain to stress. We investigate tensor basis, component, and potential-based formulations of the stress model. Violations of the second law of thermodynamics are prevented by a constraint on the weights of the neural network. We extend this framework to homogenization of materials with microstructure with a graph-based convolutional neural network that preprocesses the initial microstructure into salient features. The modeling framework is tested on large datasets spanning inelastic material classes to demonstrate its general applicability.