Accompanying dataset for the paper "On the Moreau–Jean scheme with the Frémond impact law: energy conservation and dissipation properties for elastodynamics with contact, impact and friction"

Contributions

• Vincent Acary: conceptualisation, data curation, formal analysis, funding acquisition, investigation, methodology, project administration, software, supervision, visualisation, writing – original draft, writing – review and editing.
• Nicholas Anton Collins-Craft: data curation, formal analysis, funding acquisition, investigation, methodology, software, visualisation, writing – original draft, writing – review and editing.

Data collection: period and details

• The datasets were generated numerically using Python (3.12.1) codes that in turn call the Siconos (4.5.0) program, and were generated in March and April of 2024.

Funding sources

• The work was funded by the Marie Skłodowska-Curie Actions program under the Horizon Europe research and innovation framework program (Grant Agreement ID 101064805 LEMMA). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or Horizon Europe. Neither the European Union nor the granting authority can be held responsible for them.

Data structure and information

This deposit contains the data output of the systems described in On the Moreau–Jean scheme with the Frémond impact law: Energy conservation and dissipation properties for elastodynamics with contact, impact and friction. The codes that generated this data are available in another deposit archived on Zenodo, as well as in a GitHub repository archived on Software Heritage, which is the preferred method of obtaining the codes. Two of the files in this deposit ("deformed_sliding_block_mesh.png" and "sliding_block_mesh.png") are required for one of the codes in the code deposit to run successfully ("block_mesh_plot.py", with the files assumed to be located in the folder specified in the data_folder variable of the file "path_file.py"), but the deposits are otherwise independent.

• Folder/files structure:
  • data: The data folder contains all of the results of the simulations generated using the code in workflows. It features several subfolders:
    • RockingBlock: The RockingBlock folder contains the results of the sumulations corresponding with section 5.2 of the paper, A rocking block, stored as .csv files for all quantities involved in the system.
      • MJ: The MJ folder contains the results of the simulation using the classical Moreau–Jean scheme.
      • MJF: The MJF folder contains the results of the simulation using the new Moreau–Jean scheme with the Frémond impact law.
    • Rod: The Rod folder contains the results of the simulations corresponding with section 5.1 of the paper, Impacting stick, stored as .csv files for all quantities involved in the system.
      • MJ: The MJ folder contains the results of the simulation using the classical Moreau–Jean scheme.
      • MJF: he MJF folder contains the results of the simulation using the new Moreau–Jean scheme with the Frémond impact law.
    • SlidingBlock: The SlidingBlock folder contains the results of the simulations corresponding with section 5.3 of the paper, A sliding block, stored as .csv files for the quantities that are involved in contact or are global scalar values (such as kinetic energy), and .vtk files for the quantities that are measured at each node of the finite element mesh (the velocity and displacement of each node, for example)
      • MJ: The MJ folder contains the results of the simulation using the classical Moreau–Jean scheme, with the .csv files stored at this level.
        • vtk: The vtk folder contains the nodal variables at each time step, saved as .vtk files.
      • MJF: The MJF folder contains the results of the simulation using the new Moreau–Jean scheme with the Frémond impact law, with the .csv files stored at this level.
        • vtk: The vtk folder contains the nodal variables at each time step, saved as .vtk files.
    • Wall: The Wall folder contains the results of the simulations corresponding with section 5.4 of the paper, Impact on a masonry structure, stored as .hdf5 files. In addition, a .ipynb file is included that facilitates the interpretation of the hdf5 files by rendering their structure explicit.
      • MJ: The MJ folder contains the results of the simulation using the classical Moreau–Jean scheme.
      • MJF: The MJF folder contains the results of the simulation using the new Moreau–Jean scheme with the Frémond impact law.
  • figures: The figures folder contains .pdf versions of all of the figures that are generated using the code in workflows.
  • workflows: The workflows folder contains the codes necessary to install the prerequisite Python packages, and to install Siconos with the appropriate build options and couple it with Python. This folder also contains all the codes necessary to rerun the simulations, with the specific steps to follow for installation and simulation contained in a README.md file. This folder also contains a subfolder:
    • siconos: The siconos folder contains all the files necessary to build Siconos, as well as the directory in which it is built if the install.sh script is run without any modifications.

Paper Description

The objective of this paper is to propose a time integration scheme for nonsmooth mechanical systems involving one-sided contact, impact and Coulomb friction, that respects the principles of discrete-time energy balance with positive dissipation. To obtain energetic consistency in the continuous time model when an impact occurs, we work with an impact law with friction inspired by the work of M. Frémond (Frémond, 1995, 2001, 2002, 2017) which ensures that dissipation is positive, i.e. that the Clausius–Duhem inequality is satisfied for the impulses and the velocity jumps. On this basis, we propose a time integration method based on the Moreau–Jean scheme (Jean and Moreau, 1987; Moreau, 1988) with a discrete version of the Frémond impact law, and show that this method has correct dissipation properties.