Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)

1. Micromechanical simulations using the Finite Element Method - lattice

The class and scripts refer to the Finite Element (FE) code used in (Masi, Stefanou, 2022) to generate data for training Thermdoynamics-based Artificial Neural Networks and their validation.

Usage

• The file lattice_material.py contains the classes for the constructor, assembly of lattice structures, and FE solver (Newton's method).
• lattice_prescribed_path.py contains the script for running the FE analysis of a lattice material unit cell, with periodic boundary conditions, given a prescribed strain increment path.
  • Constructor parameters: xmax, ymax, zmax are the total dimensions of the unit cell; nx, ny, nz are the number of nodes along each direction, and s is the magnitude of the perturbation (uniform spatial distribution) of the nodal coordinates
  • Boundary conditions: Dirichlet, Neumann, and periodic boundary conditions are implemented. The call is

    BC = [nodal_degree,value,"type"]

    with nodal_degree being the degree of freedom of a particular node (i.e., node's index in node_coordinates times 3 plus 3), value the prescribed value, and type the type of boundary condition "DC" for Dirichlet, "NM" for Neumann, "PR" for periodic.
• lattice_data_gen.py contains the script for running the data generation, with periodic boundary conditions, given a prescribed strain increment path.
• lattice_torsional.py contains the script for running the FE analysis of a lattice structure with fixed bottom end and imposed torsional displacement (see Masi, Stefanou, 2022).

2. Multiscale simulation with TANN - TANN - Numerical Geolab

Hands-on: employ TANN as a user-material to perform Finite Element analyses [using Numerical Geolab, 2]. The application consists of a 3D model subjected to torsional deformations. The material used represents the volume average behavior of a lattice microstructure with bars displaying elasto-plastic rate-independent behavior, with von Mises yield criterion, and kinematic hardening. For more, we refer to [1,2].

     Torsional warping: vertical displacement field due to a torsional deformation. The displacement fields were exported with the help of the third party software Paraview.

IMPORTANT: For running part of the script for the multiscale simulations, Numerical Geolab [2] software is needed. Refer to the related github repository and install the software. For more information, contact me

References

If you use this code, please cite the related papers:

[1] F Masi, I Stefanou (2022). "Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)". Computer Methods in Applied Mechanics and Engineering 398, 115190.

[2] Stathas, A. and Stefanou, I., 2023. Numerical Geolab.

@article{masi2022multiscale,
title={Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)},
author={Masi, Filippo and Stefanou, Ioannis},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={398},
pages={115190},
year={2022},
publisher={Elsevier},
doi={10.1016/j.cma.2022.115190}