Why the sum of TW.volume is not equal to the volume of pack

I suppose the periodic cell volume may not be estimated in the same way as the periodic tesselationwrapper. Do you notice the same inconsistency when you use non-periodic boundary conditions?

Dear Robert,

Thank you for your suggestion. I used non-periodic boundary and I got TW_Volume=1.0451466106445113, when the volume of pack is 1.0. It seems better but error still exists.

In addition, I got different result when I set different young, such as

TW_Volume=1.045146610644511 #young=1e6
TW_Volume=1.000684823430585 #young=1e8
TW_Volume=1.000056824921447 #young=1e10

It's interesting, the larger the young, the smaller the error.

####MWE####

from yade import pack

num_spheres=1000# number of spheres
young=1e6
compFricDegree = 3 # initial contact friction during the confining phase
mn,mx=Vector3(0,0,0),Vector3(1,1,1) # corners of the initial packing

O.materials.append(FrictMat(young=young,poisson=0.5,frictionAngle=radians(compFricDegree),density=2600,label='spheres'))
O.materials.append(FrictMat(young=young,poisson=0.5,frictionAngle=0,density=0,label='walls'))
walls=aabbWalls([mn,mx],thickness=0,material='walls')
wallIds=O.bodies.append(walls)

sp=pack.SpherePack()
sp.makeCloud(mn,mx,-1,0.3333,num_spheres,False, 0.95,seed=1) #"seed" make the "random" generation always the same
sp.toSimulation(material='spheres')

triax=TriaxialStressController(
 maxMultiplier=1.+2e4/young, # spheres growing factor (fast growth)
 finalMaxMultiplier=1.+2e3/young, # spheres growing factor (slow growth)
 thickness = 0,
 stressMask = 7,
 internalCompaction=True, # If true the confining pressure is generated by growing particles
)

newton=NewtonIntegrator(damping=0.2)

O.engines=[
 ForceResetter(),
 InsertionSortCollider([Bo1_Sphere_Aabb(),Bo1_Box_Aabb()]),
 InteractionLoop(
  [Ig2_Sphere_Sphere_ScGeom(),Ig2_Box_Sphere_ScGeom()],
  [Ip2_FrictMat_FrictMat_FrictPhys()],
  [Law2_ScGeom_FrictPhys_CundallStrack()],label="iloop"
 ),
 GlobalStiffnessTimeStepper(active=1,timeStepUpdateInterval=100,timestepSafetyCoefficient=0.8),
 triax,
 newton
]

triax.goal1=triax.goal2=triax.goal3=-10000

while 1:
  O.run(1000, True)
  unb=unbalancedForce()
  if unb<0.001 and abs(-10000-triax.meanStress)/10000<0.001:
    break

TW=TesselationWrapper()
TW.triangulate()
TW.setState()
TW.computeVolumes()

TW_Volume=0
for b in O.bodies:
    if isinstance(b.shape,Sphere):
        TW_Volume += TW.volume(b.id)

print('TW_Volume='+str(TW_Volume))

Thankyou, and then increasing the number of particles decreases or increases the discrepancy?

Looking at the source code, it looks like the original author (Bruno?) added a FIXME [1] saying we still need to properly define volumes for spheres on the borders. Looking at the function where the volume is computed for each sphere [2], it looks like fictitious vertices are neglected in the calculation of the volumes. It makes sense since these vertices are usually placed extremely far from the packing in order to generate a boundary. Further, if a cell is fictitious (if it is a boundary condition cell) then it is also neglected from the calculation. Finally, I see nothing here to consider periodicity. This all means that any volume that you might expect to be accounted for along the boundary of a packing appears to not be calculated. I guess these edge geometries are computed in the saveVTK(withBoundaries=True) function, but it would need to be copied over to this algorithm.

At the end, you should probably just take a volume as a relative value and stick with one function or the other.

[1]https://gitlab.com/yade-dev/trunk/-/blob/master/lib/triangulation/Tesselation.ipp#L1251
[2]https://gitlab.com/yade-dev/trunk/-/blob/master/lib/triangulation/Tesselation.ipp#L1196

Thanks Chareyre, that solved my question.

Hi Robert,
Thank you for your suggestions. You point out that TesselationWrapper shoudn't be used in non-periodic boundary conditions.

>increasing the number of particles decreases or increases the discrepancy?

When the volume of pack is 1.0
TW_Volume=1.05088660135025 #1000 spheres
TW_Volume=1.02397027562159 #10000 spheres
TW_Volume=1.01293294882138 #100000 spheres

Hi Bruno,
Thank you for your suggestions. I got good result with FlowEnigne in periodic boundary conditions.

 > You point out that TesselationWrapper shoudn't be used in non-periodic boundary conditions.

Nope. I said periodic conditions are not considered in TesselationWrapper.

My fault, non-periodic -> periodic :-)