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

Yuqing He, Yousef Heider, Bernd Markert

TL;DR

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.

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]

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

TL;DR

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.

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]

Paper Structure

This paper contains 13 sections, 7 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Theoretical fundamentals
  3. Data-based ML plasticity model and data preparation
  4. Overview and procedures
  5. Generation of the training datasets
  6. Mathematical expression for forward and backward pass in a single LSTM memory cell
  7. Numerical differentiation
  8. Numerical examples
  9. Simulation resutls
  10. Discussion of results and convergence
  11. Impact of initial increment size
  12. Impact of mesh fineness
  13. Summary and conclusions

Figures (7)

  • Figure 1: Illustration of the process flow: From model preparation to implementation in ABAQUS UMAT. The input file and the UMAT subroutine file can be modified within the ABAQUS components, while the implicit solver is the standard integral ABAQUS component.
  • Figure 2: Directed and informed graph representing the information flow in the machine learning-based crystal plasticity material model based on HeiderHSSuh2020_ML_offline.
  • Figure 3: Diagram illustrating the backward pass of the information flow within a single LSTM memory cell, with labeled derivatives on each edge.
  • Figure 4: Geometry of the two-dimensional initial-boundary-value problems (IBVPs) defined in ABAQUS v.2022.
  • Figure 5: Two initial-boundary-value problems (IBVPs) for comparison of the von Mieses stress components (in MPa) between the fitted isotropic hardening model and the ML-based material model in ABAQUS/Standard.
  • ...and 2 more figures