Representative Volume Element with Elastic inclusions

website: https://github.com/latug0/mfem-mgis-examples/tree/master/ex6

This example models a periodic Representative Volume Element made of two materials. Both follow the Saint Venant-Kirchhoff hyperelastic behaviour. A macroscopic deformation gradient is imposed.

By default, the Representative Volume Element is a cube made of two layers. The solution is then compared to the analytical one. The file inclusions_49.geo describes a Representative Volume Element with 49 spherical inclusions.

Build the mesh

The .geo file is in the ex6 directory. Mesh it with GMSH:

gmsh -3 inclusions_49.geo

The number of spheres and the size of the elements are parameters of the .geo file.

Run the Simulation

The first command runs the default case. The second one runs the case with inclusions:

./rve
mpirun -n 12 ./rve --mesh inclusions_49.msh --no-check

The analytical solution is only valid for the default mesh. The option --no-check disables the comparison.

Available options

Command line	Description	Default
--mesh or -m	Mesh file	cube_2mat_per.mesh
--library or -l	Material library	src/libBehaviour.so
--order or -o	Finite element order	1
--refinement or -r	Number of uniform refinements of the mesh	0
--post-processing or -pp, --no-post-processing or -no-pp	Export or not the results to Paraview	export
--check or -c, --no-check or -no-c	Compare or not the solution to the analytical solution of the two-layer cube	compare
--verbosity-level or -v	Verbosity level of the solvers	1