# TO BEGIN¶

## GEOMETRY : UNIT-CELL DESCRIPTION¶

### Definitions¶

A heterogeneous Unit-cell consists of one (or more) Material, and each Material consists of one (or more) Zone. They are defined as follows:

• All the voxels of the 3D uniform grid define the Unit-cell.
• Within a Material, all the voxels have the same behaviour law.
• Within a Zone of a Material, all the voxels have the same material properties (coefficients of the behavior law).

Note

The description of a unit-cell is often not unique (see example below). If so:

• avoid large number of Materials
• looking at outputs proposed by AMITEX_FFTP may help you to choose an appropriate description

### MaterialID and ZoneID integer fields¶

 AMITEX_FFTP needs two integer fields (or one if the other is a homogeneous field of ‘ones’) as inputs, each one representing the spatial distribution of materials and zones within materials. This example considers a unit-cell with two materials, and one material is devided into two zones (same behavior law but with different coefficients). The corresponding MaterialID and ZoneID fields are represented here:

### Example of a non-unique description¶

 Assuming a composite material with elastic isotropic matrix and inclusions, the N inclusions having the same elastic coefficients, AMITEX_FFTP is able to take into account the FIVE following descriptions: 1 material with 2 zones 1 Material with N+1 zones 2 materials with 1 zone per material 2 materials with 1 zone for the ‘matrix’ material and N zones for the ‘inclusions’ material (one per inclusion) N+1 materials with 1 zone per material

Depending on the required outputs, the recommanded descriptions are:

• Description 1 will be the most efficient with very few outputs
• Description 4 will provide per material (‘matrix’ and ‘inclusions’) statistical quantities and, on demand at given times, per inclusion statistical quantities

## HOW TO LAUNCH AMITEX_FFTP¶

Once installed (see Installation), to use AMITEX_FFTP, you must set the environment variable AMITEX_PATH, PATH (and LD_LIBRARY_PATH since v8.18.x).

For example in a file env_amitex.sh:

#!/bin/bash
export AMITEX_PATH=(amitex)
export PATH=$AMITEX_PATH/libAmitex/bin:$PATH
export LD_LIBRARY_PATH=$AMITEX_PATH/libAmitex/lib:$LD_LIBRARY_PATH


And then

$source env_amitex.sh  If you have compiled GCC and/or openMPI and/or fftw3, and used them for compiling AMITEX_FFTP (see GCC, openMPI, fftw, mfront), be sure that their respectives bin and lib (or lib64) folders are added to the PATH and LD_LIBRARY_PATH variables in the env_amitex.sh Interactively or within a batch script (for the job manager available on your machine), a simulation is launched with one of the following command lines MATEVTK="path_to/materialID.vtk" ZONEVTK="path_to/zoneID.vtk" MATEXML="path_to/material.xml" LOADXML="path_to/loading.xml" ALGOXML="path_to/algorithm.xml" RESDIR="path_to/results/ #WARNING : you must create the folder "results" before launching amitex_fftp 0. help mpirun amitex_fftp -help ! OR SIMPLY : amitex_fftp -help 1. General case mpirun amitex_fftp -nm$MATEVTK -nz $ZONEVTK -m$MATEXML -c $LOADXML -a$ALGOXML -s $RESDIR/output_file 2. One material (assumes materialID.vtk full of 1) mpirun amitex_fftp -nz$ZONEVTK -m $MATEXML -c$LOADXML -a $ALGOXML -s$RESDIR/output_file

3. One zone per material (assumes zoneID.vtk full of 1)
mpirun amitex_fftp  -nm $MATEVTK -m$MATEXML -c $LOADXML -a$ALGOXML -s $RESDIR/output_file 4. One material with one zone per voxel (assumes zoneID.vtk varying from 1 to the number of voxels) with dx=dy=dz=1. mpirun amitex_fftp -m$MATEXML -c $LOADXML -a$ALGOXML -NX nx -NY ny -NZ nz -s $RESDIR/output_file 5. One material with one zone per voxel (assumes zoneID.vtk varying from 1 to the number of voxels) mpirun amitex_fftp -m$MATEXML -c $LOADXML -a$ALGOXML -NX nx -NY ny -NZ nz -DX dx -DY dy -DZ dz -s \$RESDIR/output_file


Depending on your MPI version and/or installation, you may have to specify explicitely the number of processes and replace mpirun by mpirun -np number_of_processes.

The five possible command lines listed above correspond to the five following cases :

1. The materials and their corresponding zones are defined by materialID.vtk and zoneID.vtk.
2. The unit-cell consists of a unique material with different zones defined in zoneID.vtk.
3. The different materials defined by materialID.vtk have a unique zone (all the voxel within a material have the same properties).
4. The unit-cell consists of a unique material with one zone per voxel (the voxel dimensions are set to 1x1x1).
5. Same as 4. but the user provides the voxel dimensions

In the example above :

• the material properties, the loading & outputs and the algorithm parameters are defined in the xml files : material.xml, loading.xml and algorithm.xml (see respectively MATERIALS, LOADING&OUTPUTS, ALGORITHM).
• the rootname of the output files is output_file