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add example
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‎README.md‎

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@@ -186,3 +186,8 @@ This page uses animated gifs. In Firefox, you might want to install the plugin [
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width="200"
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title="Tensile test of an FDM structure perpendicular to the layer plane">
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](RVE/PlanarSlide)
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[<img
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src="RVE/PlaneOrtho1/exp.png"
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width="200"
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title="Tensile test of an FDM structure perpendicular to the layer plane, generalized plane strain">
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](RVE/PlaneOrtho1)

‎RVE/PlaneOrtho1/README.md‎

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# Tensile Test of FDM layers, plane and orthogonal boundaries
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Tested with CGX/CCX 2.11
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Tensile test of unidirectional FDM (3D printed) layers with load application perpendicular to the printing plane. The layed roads only partially bond between each other and to the layer below. The localized strains at the resulting notches lead to material failure at global strains much below the maximum elongation of the base material (embrittlement).
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The test specimen is a quarter unit cell out of an infinite Block of layers. This is not restricting the deformation as long as no global shear is to be applied. A uniaxial tensile test can be performed without restricting the overall transverse strain.
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+ Large displacements
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+ Plasticity
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+ The structure is parametrized using CGX valu due to it's simplicity
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+ Enforced brick shape of the unit cell using MPCs
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+ Handover of load parameters to the CCX file
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+ Handover of parameters to the gnuplot file
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| File | Contents |
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| :------------- | :------------- |
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| [RVE.fbd](RVE.fbd) | Pre-processing script for CGX (parametrized with valu commands) |
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| [post.fbd](post.fbd) | Post-processing script for CGX (stress-strain curve and deformed plot) |
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| [verify.fbd](verify.fbd) | Post-processing script for CGX (displacement plots) |
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| [pe.gnu](pe.gnu) | Gnuplot control script |
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| [Zug.inp](Zug.inp) | CCX input |
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## Preprocessing
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```
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> cgx -b RVE.fbd
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```
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The geometry consists of brick with a fillet along a single edge, representing a quarter section of an FDM road.
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The mesh is controlled by a global node distance.
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| Parameter | Value | Meaning |
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| :------------- | :------------- | :------------- |
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| `lx` | 0.02 | length in axial direction in mm |
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| `ly` | 0.5 | road width in mm |
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| `lz` | 0.25 | layer thickness in mm |
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| `rad` | 0.1 | fillet radius |
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| `le` | 0.01 | node distance on edges |
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| `ez` | 0.1 | global engineering strain in z direction |
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Boundary conditions:
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* ux = 0 at x = 0 (symmetry boundary)
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* uy = 0 at y = 0 (symmetry boundary)
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* uz = 0 at z = 0 (symmetry boundary)
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* uz = ez/100*lz at z = lz (prescribed displacement)
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* ux all equal at x = lx (parallel to yz plane)
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* uy all equal at y = ly/2 (parallel to xz plane)
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<img src="mesh.png" width="400">
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Compared to the less sophisticated [example](RVE/PlanarSlide), the model require only a fraction (a single layer) of the elements in x-direction and just one quarter of the section.
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## Solving
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```
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> ccx Zug
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> monitor.py Zug
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```
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The second command generates a convergence history plot of the solution.
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<img src="Zug.png" title="Convergence history">
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## Postprocessing
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First, let's verify the boundary conditions.
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* Uniform UX at x = lx
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* Uniform UY at y = ly
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```
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> cgx -b verify.fbd
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```
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<img src="dx.png" width="400" title="Displacement in x">
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<img src="dy.png" width="400" title="Displacement in y">
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```
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> cgx -b post.fbd
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```
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This creates a stress-strain curve and an expanded plot of the equivalent plastic strain.
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<img src="exp.png" width="400" title="Equivalent plastic strain">
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<img src="pe.png" width="500" title="Local strain and global stress">
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You can generate the curves separately using the commands:
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```
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> dat2txt.py Zug
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> gnuplot pe.gnu
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```

‎RVE/PlaneOrtho1/RVE.fbd‎

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valu lx 0.02
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valu width 0.5
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valu height 0.25
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valu rad 0.1
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valu le 0.01
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valu ez 0.1
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valu factor 0.01
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valu tol * factor le
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valu two 2
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valu ly / width two
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valu lz / height two
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# create rectangle with fillet
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pnt p0 0 0 0
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pnt py 0 ly 0
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pnt pz 0 0 lz
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pnt pyz 0 ly lz
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line l1 p0 py
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line l2 py pyz
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line l3 pyz pz
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line l4 pz p0
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fil l4 l1 rad
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# plot entity labels
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plot la all
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plus pa all
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frame
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rot x
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rot c 90
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hcpy png
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sys mv hcpy_1.png section.png
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# create surface and extrusion
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surf s1 l1 l2 l3 l4 L001
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swep all new tra lx 0 0
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# meshing
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# control nodes for plane xl
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seta control p p0
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div all auto le
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elty all te10
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mesh all
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send all abq
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plot f all n
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view elem
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# definitions of sets
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seta nodes n all
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enq nodes x0 rec 0 _ _ tol
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enq nodes y0 rec _ 0 _ tol
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enq nodes z0 rec _ _ 0 tol
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enq nodes zl rec _ _ lz tol
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enq nodes yl rec _ ly _ tol
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enq nodes xl rec lx _ _ tol
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enq nodes monitor rec 0 rad 0 tol
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send all abq nam
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# set displacement
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valu disp * ez lz
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sys echo Nzl,3,3, disp > disp.inc
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# set uy at three points in y=ly to be equal
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# define control nodes
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stack on
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enq xl n110 rec lx ly 0 tol
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valu v110 pop
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enq xl n111 rec lx ly lz tol
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valu v111 pop
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enq x0 n010 rec 0 ly 0 tol
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valu v010 pop
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enq xl n101 rec lx 0 lz tol
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valu v101 pop
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# control nodes found: v110 v111 v010 v101
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# write equations
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sys echo *equation > equations.inc
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sys echo 2 >> equations.inc
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sys echo v110 , 2, -1, v111 , 2, 1 >> equations.inc
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sys echo 2 >> equations.inc
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sys echo v010 , 2 ,-1, v111 , 2, 1 >> equations.inc
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sys echo 2 >> equations.inc
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sys echo v110 , 1, -1, v111 , 1, 1 >> equations.inc
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sys echo 2 >> equations.inc
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sys echo v101 , 1 ,-1, v111 , 1, 1 >> equations.inc
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sys echo *mpc >> equations.inc
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sys echo Plane, v111 , v110 , v101 , Nxl >> equations.inc
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sys echo *mpc >> equations.inc
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sys echo Plane, v110 , v111 , v010 , Nyl >> equations.inc
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# define reduced sets (remove control nodes)
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setr xl n v110 v111 v101
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setr yl n v110 v111 v010
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send all abq nam
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# export values to gnuplot
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valu area * lx ly
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sys echo ez= ez > ez.gnu
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sys echo area= area >> ez.gnu
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# mesh image
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plot f all n
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frame
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rot x
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rot c 90
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rot r 30
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rot u 30
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hcpy png
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sys mv hcpy_2.png mesh.png

‎RVE/PlaneOrtho1/Zug.inp‎

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*include,input=all.msh
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*include,input=x0.nam
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*include,input=y0.nam
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*include,input=z0.nam
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*include,input=xl.nam
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*include,input=yl.nam
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*include,input=zl.nam
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** symmetry
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*boundary
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Nx0, 1
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Ny0, 2
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Nz0, 3
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** parallelity constraints
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*include,input=equations.inc
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** material definition
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*material, name=ABS
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*elastic
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2000,0.3,0
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*density
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1e-9
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*plastic
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20, 0, 0
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30, 2, 0
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*solid section, elset=Eall, material=ABS
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*STEP, NLGEOM,inc=200
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*STATIC
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0.01,1,,0.1
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** displacement control at top
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*boundary
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*include,input=disp.inc
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*el file
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S,PEEQ
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*node file
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U
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*node print, totals=only, nset=Nz0
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RF
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*end step

‎RVE/PlaneOrtho1/Zug.png‎

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‎RVE/PlaneOrtho1/dx.png‎

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‎RVE/PlaneOrtho1/dy.png‎

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‎RVE/PlaneOrtho1/exp.png‎

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‎RVE/PlaneOrtho1/hcpy_3.png‎

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‎RVE/PlaneOrtho1/mesh.png‎

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