# uncertainty in the shear behavior of material

Hello All,

I was encountered to a problem in my dem modeling. I want to simulate the bulk behavior of material. Due to reach this goal, I have to choose a number of particles which could represent the bulk behavior as similar as experiment. I did two type of simulation.
in the first one, I put the particles in the box and the the box faces compress the paricles, after in the x and y direction, stress remain constant and in the z direction, we increase stress and plot the strain-stress in z direction. Due to initial conditions (randomness of initial position of particles) we will reach to different results in each realization. The code is as below:

from datetime import datetime

O.periodic=True
O.cell.refSize=(2e-1,2e-1,2e-1)

O.materials.append(CohFrictMat(normalCohesion= 1e20, shearCohesion= 1e20, isCohesive= True, young=6.81e8, density=1377.5, poisson=0.3, frictionAngle= 0.31, fragile=False, label='Coke'))

nums=['t']

mats=['Coke']

coke=(5e-3,3000)

nums=pack.SpherePack()

nums.makeCloud((0,0,0),(2e-1,2e-1,2e-1),rMean=coke[0],rRelFuzz=0,num=coke[1])

O.bodies.append([utils.sphere(c,r,material=mats[0],color=(0,0,1)) for c,r in nums])

sigmaIso=-1e5

O.engines=[
ForceResetter(),

InsertionSortCollider([Bo1_Sphere_Aabb()]),
InteractionLoop(
[Ig2_Sphere_Sphere_ScGeom()],
[Ip2_FrictMat_FrictMat_FrictPhys()],
[Law2_ScGeom_FrictPhys_CundallStrack()]
),

PeriTriaxController(label='triax',
dynCell=True,maxStrainRate=(1,1,1),
maxUnbalanced=.01,relStressTol=1e-3,
doneHook='compactionFinished()'
),
NewtonIntegrator(damping=0.4),
PyRunner(command='history()',iterPeriod=1000,label='recorder'),
]

O.dt=1e-6

O.saveTmp()

def compactionFinished():

O.cell.trsf=Matrix3.Identity
triax.goal=(sigmaIso,sigmaIso,-0.5)
triax.maxStrainRate=(0.1,0.1,0.1)
triax.doneHook='triaxFinished()'
triax.maxUnbalanced=1
dataOld = plot.data
plot.saveDataTxt('RVE3000-iso_part-e5-5.txt')
plot.data = {}
plot.plot()

def history():
sxx=-triax.stress[0],syy=-triax.stress[1],szz=-triax.stress[2],
exx=-triax.strain[0],eyy=-triax.strain[1],ezz=-triax.strain[2],
sxz=-0.5*(triax.stress[2]+triax.stress[0]), ev=(triax.strain[2]+triax.strain[1]+triax.strain[0]),
q=-(triax.stress[2]-triax.stress[1]), p=-(triax.stress[2]+triax.stress[1]+triax.stress[0])/3 ,
D=(triax.stress[2]-triax.stress[1])/sigmaIso,
R=3*(triax.stress[2]-triax.stress[1])/(triax.stress[2]+triax.stress[1]+triax.stress[0]+1e-2),
por=porosity(),i=O.iter,)

print 'porosity:', porosity()
print 'iteration', O.iter

O.run(8000000,True)

plot.saveDataTxt('RVE3000-dev_part-e5-5.txt')
plot.plots={'ezz':('szz')}
plot.plot()

def triaxFinished():
print 'Compaction finished'
O.pause()

In the second one, I made the sample first with the code below:

from datetime import datetime

O.periodic=True
O.cell.refSize=(2e-1,2e-1,2e-1)

O.materials.append(CohFrictMat(normalCohesion= 1e20, shearCohesion= 1e20, isCohesive= True, young=6.81e8, density=1377.5, poisson=0.3, frictionAngle= 0.31, fragile=False, label='Coke'))

nums=['t']

mats=['Coke']

coke=(5e-3,3000)

nums=pack.SpherePack()

nums.makeCloud((0,0,0),(2e-1,2e-1,2e-1),rMean=coke[0],rRelFuzz=0,num=coke[1])

O.bodies.append([utils.sphere(c,r,material=mats[0],color=(0,0,1)) for c,r in nums])

sigmaIso=-1e5

O.engines=[
ForceResetter(),

InsertionSortCollider([Bo1_Sphere_Aabb()]),
InteractionLoop(
[Ig2_Sphere_Sphere_ScGeom()],
[Ip2_FrictMat_FrictMat_FrictPhys()],
[Law2_ScGeom_FrictPhys_CundallStrack()]
),

PeriTriaxController(label='triax',
dynCell=True,maxStrainRate=(1,1,1),
maxUnbalanced=.01,relStressTol=1e-3,
doneHook='compactionFinished()'
),
NewtonIntegrator(damping=0.4),
PyRunner(command='history()',iterPeriod=1000,label='recorder'),
]

O.dt=1e-6

O.saveTmp()

def compactionFinished():
print 'Finished'
O.pause()
plot.saveDataTxt('Uncertainty-Pre-compact3000.txt')
plot.data = {}

O.run(1500000,True)

and after that, I compress the sample of "Pre-compact3000.yade" in the z direction and plot the stress-strain in the z direction with code below:

from datetime import datetime

sigmaIso=-1e5

def compactionFinished():

O.cell.trsf=Matrix3.Identity
triax.goal=(sigmaIso,sigmaIso,-0.5)
triax.maxStrainRate=(0.1,0.1,0.1)
triax.doneHook='triaxFinished()'
triax.maxUnbalanced=1
dataOld = plot.data
# plot.saveDataTxt('iso_part-e4.txt')
plot.data = {}
plot.plot()

def history():
sxx=-triax.stress[0],syy=-triax.stress[1],szz=-triax.stress[2],
exx=-triax.strain[0],eyy=-triax.strain[1],ezz=-triax.strain[2],
sxz=-0.5*(triax.stress[2]+triax.stress[0]), ev=(triax.strain[2]+triax.strain[1]+triax.strain[0]),
q=-(triax.stress[2]-triax.stress[1]), p=-(triax.stress[2]+triax.stress[1]+triax.stress[0])/3 ,
D=(triax.stress[2]-triax.stress[1])/sigmaIso,
R=3*(triax.stress[2]-triax.stress[1])/(triax.stress[2]+triax.stress[1]+triax.stress[0]+1e-2),
por=porosity(),i=O.iter,)

print 'porosity:', porosity()
print 'iteration', O.iter

O.run(5000000,True)

plot.saveDataTxt('Uncertainty-compect300-6.txt')
plot.plots={'ezz':('szz')}
plot.plot()

def triaxFinished():
print 'Compaction finished'
O.pause()

However, when I run the code again, I reach to a different results. But we know that the initial sample is the same.
Where does this uncertainty come from?Why the stress-strain curves are different for the same initial sample?

Best Reagrds

Alireza

## Question information

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Status:
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Solved by:
Robert Caulk
Solved:
2019-08-27
Last query:
2019-08-27
2019-08-27
 Robert Caulk (rcaulk) said on 2019-08-27: #1

>I reach to a different results.

Quantification would be quite helpful. Probably [1].