• Finding metamaterial structure with negative poisson's ratio using ABAQUS and MOP evolutionary algorithm approaches.
• In addition to structure with negative poisson's ratio, other types of material structure can be created by varying version fitness values definitions.
• The definition of fitness value for negative Poisson's ratio is well defined in auxeticmop.ParameterDefinitions.fitness_definitions['ver3'].

• The script full_scripts.py or auxeticmop.sample_scripts.full_steps.run() generates 1/8 structure of unit cell using ABAQUS CAE software by genetic algorithm. This script is especially for finding mechanical meta-material structure consisting of 3D voxels.

• GUI is provided for getting initial parameters for ABAQUS, and plotting results when a generation work is done.

  • Related contents: auxeticmop.GraphicUserInterface

• Python script running on ABAQUS is located in auxeticmop.AbaqusScripts. This will run only on ABAQUS-embedded python interpreter, and maybe the version is 2.7.15. Other scripts are running on newer Python.

• Non-dominated Sorting Genetic Algorithm(NSGA) is used to validate and assess fitness values of generated topologies.

  • Related contents: auxeticmop.GeneticAlgorithm, auxeticmop.MutateAndValidate

• Auxetic cell

• 10 by 10 by 10 voxels per 1/8 cell.
• Negative negative poisson's ratio structure

• GUI example

• Building a GUI using tkinter and matplotlib
• Receiving parameter values required for ABAQUS analysis and GA setting from the user
• The Pareto optimization solution and hyper volume value calculated from the Main Process are input in real time and output as a graph.

Before installing this package, ABAQUS CAE must be installed.

To install the current release via PyPI with Python version >=3.6 and <3.11:

$ pip install auxeticmop

... or to install the current release via anaconda with Python version >=3.6 and <3.11:

$ conda install -c cosogi auxeticmop

$ python

>>> from auxeticmop.sample_scripts import full_steps
>>> if __name__ == '__main__':
  ...   full_steps.run()

>>> from auxeticmop import ParameterDefinitions
>>> dir(ParameterDefinitions)
Output: ['FitnessDefinitions', 'GuiParameters', 'JsonFormat', 'Parameters', 'Union', '__builtins__',
         '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__',
         'dataclass', 'exported_field_outputs_format', 'fitness_definitions', 'material_property_definitions',
         'np', 'radiobutton_name_dict', 'translate_dictionary']

• Go to auxeticmop.ParameterDefinitions and use editor to directly customize parameters.
• If using VS code, press F12, if using Pycharm, press Ctrl+B to go to file.

All Steps are included in auxeticmop.GeneticAlgorithm.NSGAModel.evolve_a_generation().

1. Generate offspring topologies from parent topologies.

• Related contents: auxeticmop.GeneticAlgorithm.NSGAModel.generate_offspring_topologies()

2. Analyze displacements, reaction forces, or other mechanical properties of offspring topologies using ABAQUS CAE.

• Related contents: auxeticmop.Network.start_abaqus_cae(), auxeticmop.Network.request_abaqus(), auxeticmop.AbaqusScripts

3. Evaluate fitness values of parents and offsprings.

• Related contents: auxeticmop.PostProcessing.evaluate_all_fitness_values()

4. Select desired topologies which fits pareto-front(non-dominated) points and export these as next parent.

• Related contents: auxeticmop.PostProcessing.selection()

5. Redo steps 1~4 for next generations. Iterations of all generations are done in auxeticmop.GeneticAlgorithm.NSGAModel.evolve().

• 3D print-ability without supports, maximum overhang distance is also considered.
  • Related contents: auxeticmop.MutateAndValidate.make_3d_print_without_support
• Allowing only Face-to-Face contact between voxels.
  • Related contents: auxeticmop.MutateAndValidate.make_voxels_surface_contact
• All six faces of structure are connected as one tree, thereby not allowing force-free structure inside an unit cell.
  • Related contents: auxeticmop.MutateAndValidate.one_connected_tree

• Those two fitness values(objective functions) should go lower.
• The fitness value definitions are well organized in auxeticmop.ParameterDefinitions.fitness_definitions.
• You can choose the version of fitness value evaluation in GUI.

• vol_frac: Volume fraction in cell (0~1)
• k: penalty coefficient
• k: penalty coefficient

• [Language] Python, with version >=3.6 and <3.11.
• Version dependency
  • numba for Python 3.11 is not supported yet.
  • dataclass is not supported under Python 3.6
• [External libraries] numpy, numba, scipy, matplotlib, aiofiles, dataclasses
• [Other software] ABAQUS CAE