Periodic

RVE with periodic boundary conditions

Tested with CGX 2.19 / CCX 2.19

This is a generic RVE of a fiber-matrix compound.

• Brick-shaped unit cell
• Structured mesh
• Location-based assignment of material to elements
• Periodic boundary conditions applied via helper script periodic.py

Todo:

• Output of the average nominal stress
• Comfortable specification of load histories

File	Contents
RVE.fbd	Pre-processing script for CGX (parametrized with valu commands)
post.fbd	Post-processing script for CGX (stress-strain curve and deformed plot)
Solve.inp	CCX input
test.py	Python script to run the full simulation

Preprocessing

> cgx -b RVE.fbd
> periodic.py all.msh

The RVE represents a matrix material with unidirectional fibers arranged at a rectangular grid. Dimension lx is irrelevant, as the material is uniform in x direction. Dimensions ly and lz represent the fiber grid lengths.

The mesh consists of C3D8I elements and is controlled by a global node distance.

Parameter	Value	Meaning
lx	1	length in x in mm
ly	1	length in y in mm
lz	1	length in z in mm
rad	0.2	fiber radius
le	0.1	node distance

Constraints:

• periodic.py produces set definitions for control nodes and the equations for periodicity.
• Components of the average deformation gradient or of the average nominal stress (first Piola-Kirchhoff stress) can be specified as displacements or forces at the control nodes. In the given example, the deformation gradient is a 20% stretch in x direction and a 20% shear on the y-plane in z direction. The components are prescribed as (x means unconstrained)

1 + 0.2    x       x
   0       x       0
   0      0.2      x

Given the edge length of 1, the above deformation gradient can be prescribed using

*boundary
nx,1,1,0.2
nx,2,3
ny,3,3,0.2
nz,2,2,0

Solving

> ccx Solve

Postprocessing

Plots of the equivalent stress, the periodicity of the deformation is visible.

> cgx -b post.fbd