DOI: 10.5281/zenodo.17857583
title: A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains (Source code and data)

description: This repository accompanies the work “A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains”. It contains the complete implementation of the neural network–based constitutive modeling framework presented in the paper. The provided code includes neural network models for anisotropic and inelastic materials, their training scripts, and finite element simulations using the learned constitutive laws.

The directory NN_Ani_Inelastic_Just_Code/ is organized into three main modules (the directory NN_Ani_Inelastic/ includes all results such as network weights, ParaView files, and training data ):

01_NN/ – Neural Network constitutive models.This folder contains the core implementation of the inelastic constitutive artificial neural networks (iCANNs) used for isotropic and anisotropic materials.





ConstiNNscripts/: Definitions of neural constitutive models, recurrent architectures (RNN_iCANN), cell formulations, and exponential map integrators.




NNscripts/: Supporting network architectures such as ICNNs, monotonic networks, and helper utilities for constraint application.




CONTIscripts/: Continuum mechanics helper functions, including invariants, deviatoric projections, and generating functions.




TRAINscripts/: Training routines for different constitutive settings (e.g., isotropic vs. one-fiber anisotropy, liquid-EM models, exponential map integrators).




train_PWTEH_.py* and eval_PWTEH_.py*: Top-level training and evaluation scripts for plane strain problems.




RESULTS/ and DATA/: Folders prepared for storing output data and model checkpoints.



02_FEM/ – Finite element simulations using the trained neural constitutive models.This module provides the finite element solver and scripts to run benchmark problems such as the Cook’s membrane with and without holes.





FEMscripts/: Core FEM routines, including mesh handling, shape functions (Q1 elements), time integration, and neural-network–based material models.




00_meshes/: Input mesh files (.inp) for the test cases (e.g., Cook with hole, plate with two holes, PWTEH geometry).




main_CookWH_.py*: Simulation scripts for isotropic and anisotropic neural materials as well as purely mechanical reference cases.




01_results/: Folder intended for storing FEM results.



03_RNN/ – Temporal constitutive models using recurrent architectures.This folder includes implementations and training scripts for recurrent neural networks capturing history-dependent (inelastic) material behavior.





RNN.py and LiNN.py: Core recurrent formulations for incremental constitutive updates.




main_RNN_ani.py and main_LiNN_ani.py: Training and evaluation scripts for anisotropic materials.




main_RNN_iso.py and main_LiNN_iso.py: Isotropic counterparts.




run_training.sh: Example shell script for automated model training.



Version v2 / NN_Ani_Inelastic_NoisyThis dataset contains the results and implementation of the constitutive Neural Networks for isotropic and anisotropic material behavior.Both the Liquid Neural Network implementation and the (explicit) exponential integrator routines are provided.In addition, the data for each element and the routine to generate the noisy data is included in the dataset.

The requirements.txt file lists all necessary Python dependencies for reproducing the results.

This dataset provides the complete codebase for training, evaluating, and coupling neural constitutive models with a finite element framework. It enables reproduction of the results shown in the paper for both isotropic and anisotropic inelastic materials, including path-dependent and rate-dependent responses modeled through RNN-based architectures. The provided scripts and model definitions can be directly extended for new material systems or benchmark problems in computational mechanics.