An Eulerian Framework for Modeling Visco-Plasticity and Isotropic and Directional Material Hardening Utilizing Neural Networks

Abstract

A neural network is inserted into a theoretical framework for modeling the inelastic behavior of materials. The neural network replaces functional expressions for such phenomena as isotropic and directional hardening and viscoplasticity. The theoretical framework, into which the neural network is inserted, is Eulerian in the sense that all state variables are defined in the current state of the material, and the framework is independent of history variables, such as plastic strain, accumulated equivalent plastic strain, etc. The neural network-based model is compared to and trained to reproduce the uniaxial tension response of theoretical reference solutions as well as experimental results. The neural network-based model is able to reproduce the reference results with excellent precision. Also, the neural network-based model was implemented as a VUMAT in Abaqus together with one of the theoretical reference models. Deformation of a plate with a hole in it was simulated, and the outcome from the reference model and the trained neural network-based model was compared. The solutions, in terms of von Mises stress and accumulated equivalent plastic strain, were very similar. Hence, it seems like training the neural network model by use of uniaxial stress data is sufficient for being able to make accurate 3D predictions.