  We propose a physics informed, neural network-based elasto-viscoplasticity
(NN-EVP) constitutive modeling framework for predicting the flow response in
metals as a function of underlying grain size. The developed NN-EVP algorithm
is based on input convex neural networks as a means to strictly enforce
thermodynamic consistency, while allowing high expressivity towards model
discovery from limited data. It utilizes state-of-the-art machine learning
tools within PyTorch's high-performance library providing a flexible tool for
data-driven, automated constitutive modeling. To test the performance of the
framework, we generate synthetic stress-strain curves using a power law-based
model with phenomenological hardening at small strains and test the trained
model for strain amplitudes beyond the training data. Next, experimentally
measured flow responses obtained from uniaxial deformations are used to train
the framework under large plastic deformations. Ultimately, the Hall-Petch
relationship corresponding to grain size strengthening is discovered by
training flow response as a function of grain size, also leading to efficient
extrapolation. The present work demonstrates a successful integration of neural
networks into elasto-viscoplastic constitutive laws, providing a robust
automated framework for constitutive model discovery that can efficiently
generalize, while also providing insights into predictions of flow response and
grain size-property relationships in metals and metallic alloys under large
plastic deformations.

Computational Engineering, Finance, and Science