Example: polyx_mfront

The example described below demonstrates on a large polycrystalline simulation:

  • The ability of AMITEX_FFTP to take advantage of massive parallelism (simulation performed on 1024 cores)
  • The ability of AMITEX_FFTP to take into account a behavior law elaborated with the code generator MFront developed at CEA (http://tfel.sourceforge.net/documentations.html)

The algorithm converged with a total number of 102 iterations and the computation time, on 1024 cores (64 nodes, bi-processors Sandy Bridge E5-2670), was approximatively 4 hours.

The microstructure (A), the average behavior (B) and the local stress (C) and strain (D) fields are presented below.

Microstructure (A) Average behavior (B)

Local stress (C) Local Strain (D)


The unit-cell consists of 42875 grains (Voronoļ tessellation).

The unit-cell is discretized with a 1024x1024x1024 grid (almost 30x30x30 voxels per grain).

Behavior law

The behavior law accounts for crystalline plasticity for Cubic Face Centered crystals in a small perturbation framework (description in the Code_Aster documentation R5.03.11). The implementation is provided with the code generator MFront (http://tfel.sourceforge.net/documentations.html) using the so-called “UMAT” interface, also compatible with the finite element code CAST3M (http://www-cast3m.cea.fr/). The material parameters are those furnished with the MFront code with 42875 crystalline orientations (one per grain) randomly distributed with an isotropic crystallographic texture.


The number of internal variables (required at each voxel) is 54.

The numerical integration of such behaviors is quite “heavy”.


The applied loading is a tensile test loading (axial strain component and zero-stress on the five other components are imposed), at a strain rate of \(10^{-4}s^{-1}\) until 1%.

The loading is uniformly discretized in 100 steps (1 second per step).


The algorithm is the classical fixed-point algorithm. The discrete Green operator is based on a cubic filter (of size one voxel).

The criterion (stress divergence and applied load) is \(10^{-4}\).