DOI: 10.5281/zenodo.16926097
title: Dataset: A dual-stage constitutive modeling framework based on finite strain data-driven identification and physics-augmented neural networks

description: ############################################################## README###########################################################

Dataset for benchmark test of a perforated plate under uniaxial tension(based on: *A dual-stage constitutive modeling framework based on finite strain data-driven identification and physics-augmented neural networks*)

############################################################## REFERENCE###########################################################

If you use this dataset, please cite the associated paper:

Lennart Linden, Karl Kalina, Jörg Brummund, Brain Riemer, Markus Kästner "A dual-stage constitutive modeling framework based on finite strain data-driven identification and physics-augmented neural networks"  Computer Methods in Applied Mechanics and Engineering (CMAME), 2025.

This dataset corresponds to Section 4.2: *Benchmarking the DDI formulations with ideal data*.

############################################################## AUTHORS & CONTACT###########################################################

Dataset prepared by: Lennart Linden, Karl Kalina, Jörg Brummund, Brain Riemer, Markus KästnerAffiliation: Chair of Computational and Experimental Solid Mechanics, TU Dresden, Dresden, 01069, GermanyContact: lennart.linden@tu-dresden.de

Version: v1.0 (August 2025)

############################################################## LICENSE###########################################################

© 2025 Lennart Linden, Karl Kalina, Jörg Brummund, Brain Riemer, Markus Kästner. All rights reserved.

This dataset is licensed under Creative Commons Attribution-NoDerivatives (CC BY-ND 4.0).More information: https://creativecommons.org/licenses/by-nd/4.0/

############################################################## DESCRIPTION###########################################################

- Geometry: Thin perforated disk (plane stress assumption),   domain of interest: 100 mm × 100 mm × 5 mm- Loading: Uniaxial tensile test, displacement at the boundary   increased linearly in all increments    - number of increments:               n_increments = 10- Material model: Neo-Hookean,     - material parameter:        - Young’s modulus                    E = 1000 kPa        - Poisson’s ratio                         ν = 0.3- Discretization: Linear triangular finite elements    - number of nodes:                       n_nodes = 4403    - number of elements:                  n_elements = 8444    - number of quadrature points:    n_quadrature_points = 8444- Software: in-house code was used

############################################################## DIRECTORY STRUCTURE###########################################################

benchmark_perforated_disk_uniaxial_v1.0/├── README.txt└── Data/    ├── mesh.msh                               # Finite element mesh    ├── displacement.npy                   # Nodal displacements    ├── force.npy                                # External nodal forces    ├── thickness_initial.npy               # Initial plate thickness    ├── thickness.npy                         # Plate thickness at quadrature points per increment    ├── deformation_gradient.npy     # In-plane deformation gradient    ├── strain.npy                               # Euler-Almansi strain field    ├── stress.npy                               # Cauchy stress field

############################################################## DATA FORMAT###########################################################

All files (except mesh.msh) are stored as NumPy binary files (.npy).

############################################################## FILE DETAILS###########################################################

- mesh.msh    Finite element mesh in Gmsh format.

- displacement.npy    Array shape: (n_increments, 2*n_nodes)    Displacements (ux, uy) per node and increment.

- force.npy    Array shape: (n_increments, 2*n_nodes)    External forces (fx, fy) per node and increment.

- thickness_initial.npy    Scalar: initial plate thickness.

- thickness.npy    Array shape: (n_increments, n_quadrature_points)    Plate thickness at quadrature points for each increment.

- deformation_gradient.npy    Array shape: (n_increments, n_quadrature_points, 4)    In-plane deformation gradient components F11, F12, F21, F22.

- strain.npy    Array shape: (n_increments, n_quadrature_points, 4)    Strain components e11, e22, e12, e33.

- stress.npy    Array shape: (n_increments, n_quadrature_points, 3)    Stress components sigma11, sigma22, sigma12.

############################################################## USAGE NOTES###########################################################

Data can be loaded in Python using NumPy:

    import numpy as np    displacements = np.load("Data/displacements.npy")

All quantities are provided in SI units:- Length in millimeter (mm)- Forces / 1000 in newton (N)- Stresses in kilopascal (kPa)