Embedding an ANN-Based Crystal Plasticity Model into the Finite Element Framework using an ABAQUS User-Material Subroutine

TL;DR

This paper introduces a practical method for embedding neural network-based crystal plasticity models into finite element simulations via ABAQUS UMAT subroutines, enabling data-driven, multiscale material modeling.

Contribution

It presents a novel approach to integrate trained neural networks into FEM as a constitutive law using UMAT, applicable to complex inelastic material behaviors.

Findings

Neural network models can be effectively embedded in FEM simulations.

The method improves accuracy in modeling complex material responses.

Implementation details and source code are provided for reproducibility.

Abstract

This manuscript presents a practical method for incorporating trained Neural Networks (NNs) into the Finite Element (FE) framework using a user material (UMAT) subroutine. The work exemplifies crystal plasticity, a complex inelastic non-linear path-dependent material response, with a wide range of applications in ABAQUS UMAT. However, this approach can be extended to other material behaviors and FE tools. The use of a UMAT subroutine serves two main purposes: (1) it predicts and updates the stress or other mechanical properties of interest directly from the strain history; (2) it computes the Jacobian matrix either through backpropagation or numerical differentiation, which plays an essential role in the solution convergence. By implementing NNs in a UMAT subroutine, a trained machine learning model can be employed as a data-driven constitutive law within the FEM framework, preserving multiscale information that conventional constitutive laws often neglect or average. The versatility of this method makes it a powerful tool for integrating machine learning into mechanical simulation. While this approach is expected to provide higher accuracy in reproducing realistic material behavior, the reliability of the solution process and the convergence conditions must be paid special attention. While the theory of the model is explained in [Heider et al. 2020], exemplary source code is also made available for interested readers [https://doi.org/10.25835/6n5uu50y]