Commented Examples

All the examples presented in this section can be found in the git repositories: https://github.com/latug0/mfem-mgis-examples and https://github.com/rprat-pro/mm-opera-hpc (developed as part of operaHPC project).

TensileTest 

website : https://github.com/latug0/mfem-mgis-examples/tree/master/ex1

Description:

Illustration of the start of the TensileTest simulation.

Warning

Complet the description

Problem Solved

Export the internal value name plasticity strain

Solver : Conjugate Gradient (default)
Preconditioner : Depends on the solver

The default is plasticity, behavior law parameter are defined into the lib loaded.

Element:
- Family H1
- Order 1

Run This Simulation

mpirun -n 10 ./UniaxialTensileTestEx -m cube.mesh -l  src/libBehaviour.so -b Plasticity -r Plasticity.ref -ls 1 -p 1 -v EquivalentPlasticStrain

Available options

To customize the simulation, several options are available, as detailed below.

Command line	Descritption
–mesh or -m	specify the mesh “.msh” used (default = inclusion.msh)
–refinement or -r	The reference file (default = Plasticity.ref)
–behaviour or -b	Name of the behaviour law (default = Plasticity)
–internal-state-variable or -v	Internal variable name to be post-processed (default = EquivalentPlasticStrain)
–library or -l	Material library (default = src/libBehaviour.so)
–linearsolver or -ls	identifier of the linear solver: 0 -> CG, 1 -> GMRES, 2 -> UMFPack (serial), 3-> MUMPS(serial), 2 -> HypreFGMRES (//), 3 -> HyprePCG (//), 4 -> HypreGMRES (//).
–order or -o	Finite element order (polynomial degree) (default = 2)
–parallel or -p	run parallel execution (default = 0, serial)

Ssna303 Example (2D and 3D)

This tutorial deals with a 2D (plane strain) tensile test (ex2) and 3D (ex4) on a notched beam modeled by finite-strain plastic behavior. See the tutorial section.

website 2D example: https://github.com/latug0/mfem-mgis-examples/tree/master/ex2
website 3D example : https://github.com/latug0/mfem-mgis-examples/tree/master/ex4

Illustration of the start of the ssna303 simulation.

Satoh 

website: https://github.com/latug0/mfem-mgis-examples/tree/master/ex5

Description:

Modelling plate of length 1 in plane strain clamped on the left and right boundaries and submitted to a parabolic thermal gradient along the x-axis. (source code 5)

Illustration of the displacement of the plate.

Problem solved

This test models a 2D plate of lenght 1 in plane strain clamped on the left
and right boundaries and submitted to a parabolic thermal gradient along the
x-axis:

- the temperature profile is minimal on the left and right boundaries
- the temperature profile is maximal for x = 0.5

This example shows how to define an external state variable using an
analytical profile.

Solver : UMFPackSolver
Preconditioner : None

Elastic behavior law parameters :
[ parameters       , material ]
[ Young Modulus    , 150e9    ];
[ Poisson Ratio    , 0.3      ];
[ Temperature      , 293.15   ];

Element:
- Family H1
- Order 2

Run the simulation

Paramerters are hardcode into this example.

./SatohTest

Note

If you want to run this example in parallel, you’ll have to change the solver too.

Representative Volume Element with Elastic inclusions 

Simulation of a Representative Volume Element (RVE) with a non-linear elastic behavior law. A geometry mesh is provided : “inclusions_49.geo”. The mesh can be generated using the following command: gmsh -3 inclusions_49.geo. By modifying the parameters within the .geo file, such as the number of spheres and the size of the element mesh, you can control and customize the simulation accordingly. (code source: ex6)

Build the mesh

Use GMSH to mesh the geometry. Files .geo is in the depository ex6. Command line:

# generate the .msh file with GMSH
gmsh -3 inclusions_49.geo

Run the Simulation

mpirun -n 12 ./rve --mesh inclusions_49.msh --verbosity-level 0

Available options

To customize the simulation, several options are available, as detailed below.

Command line	Descritption
–mesh or -m	specify the mesh “.msh” used (default = inclusion.msh)
–refinement or -r	refinement level of the mesh (default = 0)
–order or -o	Finite element order (polynomial degree) (default = 2)
–verbosity-level or -v	choose the verbosity level (default = 0)
–post-processing or -p	run post processing step (default = 1)

Representative Volume Element of Combustible Mixed Oxides for Nuclear Applications 

This simulation represents an RVE of MOx (Mixed Oxide) material under uniform macroscopic deformation. The aim of this simulation is to reproduce and compare the results obtained by (Fauque et al., 2021; Masson et al., 2020) who used an FFT method. (source code: ex7)

Problem solved

Problem : RVE MOx 2 phases with elasto-viscoplastic behavior laws

Parameters :

start time = 0
end time = 5s
number of time step = 40

Imposed strain tensor :
        [ -a/2 ,   0  ,  0 ]
eps  =  [   0  , -a/2 ,  0 ]
        [   0  ,   0  ,  a ]
with a = 0.012

Solver : HyprePCG
Preconditioner : HypreBoomerAMG

Moduli and Norton behavior law parameters :
[ parameters       , inclusions   , matrix ]
[ Young Modulus    , 8.182e9  , 2*8.182e9  ];
[ Poisson Ratio    , 0.364    , 0.364      ];
[ Stress Threshold , 100.0e6  , 100.0e12   ];
[ Norton Exponent  , 3.333333 , 3.333333   ];
[ Temperature      , 293.15   , 293.15     ];

Element :
- Familly H1
- Order 2

Illustration of a RVE with 634 spheres after 5 seconds.

How to run the simulation “RVE MOX”

Build the mesh

The mesh is generated with MEROPE and GMSH through the following steps:

First step, use MEROPE to generate a .geo file using the RSA algorithm. Scripts are in directory script_merope. Command line:

# generate .geo file with MEROPE
python3 script_17percent_minimal.py

Second step, use GMSH to mesh the geometry. Files .geo are in the directory file_geo. Command line:

# generate the .msh file with GMSH
gmsh -3 OneSphere.geo

Run the simulation

Run a minimal version of the simulation

In order to run the simulation in sequential computing mode, use the command line:

# run the simulation by specifying the mesh with --mesh option
./mox2 --mesh OneSphere.msh

With MPI + Petsc:

mpirun -n 2 mox2 -m mesh/OneSphere.msh -o 1 --use-petsc true --petsc-configuration-file petscrc

Available options

To customize the simulation, several options are available, as detailed below.

Command line	Descritption
–mesh or -m	Specify the mesh “.msh” used (default = inclusion.msh)
–refinement or -r	Refinement level of the mesh (default = 0)
–order or -o	Finite element order (polynomial degree) (default = 2)
–verbosity-level or -v	Choose the verbosity level (default = 0)
–post-processing or -p	Run post processing step (default = 1)
–use-petsc	Activate petsc if petsc is availabled
–petsc-configuration-file	Name of the Petsc source file

Example of customized simulation:

# run the simulation in sequential computing mode with various options
./mox2 -r 2 -o 3 --mesh OneSphere.msh

Parallel computing mode

The simulation can be run in parallel computing mode by using the command:

# run the simulation by specifying the mesh with --mesh option
mpirun -n 12 ./mox2 --mesh 634Spheres.msh

Simulation can be run on supercomputers. The command depends on the server manager. For example, on Topaze, a CCRT-hosted supercomputer co-designed by Atos and CEA, the commands are :

ccc_mprun -n 8 -c 1 -p milan ./mox2 -r 0 -o 3 --mesh OneSphere.msh
ccc_mprun -n 2048 -c 1 -p milan ./mox2 -r 2 -o 1 --mesh 634Sphere.msh

Post-processing of simulation data

The aim of this exercise is to reproduce the simulation results of (Fauque et al., 2021; Masson et al., 2020). To this end, the average stresses in the z-axis direction (SZZ) will be analyzed. The reference values, obtained by (Fauque et al., 2021; Masson et al., 2020), can be found in the directory results, file res-fft.txt (Average stress versus time).

Extract simulation data from MMM

The avgStress post-processing file generated by MMM contains average stress values as a function of time, by material phase. MMM simulation data are available: results/res-mfem-mgis-onesphere-o3.txt and results/res-mfem-mgis-634sphere-o2.txt.

For example, the average stress SZZ over the RVE (composed of 83% matrix and 17% inclusion) can be calculated with the awk command under unix:

awk '{if(NR>13) print $1 " " 0.83*$4+0.17*$10}' avgStress > res-mfem-mgis.txt

Display results with gnuplot

gnuplot> plot "res-fft.txt" u 1:10 w l title "fft"
gnuplot> replot "res-mfem-mgis.txt" u 1:2 w l title "mfem-mgis"

Commented Examples

TensileTest

Description:

Problem Solved

Run This Simulation

Available options

Ssna303 Example (2D and 3D)

Satoh

Description:

Problem solved

Run the simulation

Representative Volume Element with Elastic inclusions

Build the mesh

Run the Simulation

Available options

Representative Volume Element of Combustible Mixed Oxides for Nuclear Applications

Problem solved

How to run the simulation “RVE MOX”

Build the mesh

Run the simulation

Run a minimal version of the simulation

Available options

Parallel computing mode

Post-processing of simulation data

Extract simulation data from MMM

Display results with gnuplot

TensileTest 

Satoh 

Representative Volume Element with Elastic inclusions 

Representative Volume Element of Combustible Mixed Oxides for Nuclear Applications 