# Normal stiffness of contact under tension

Hi guys,

I am a new user of Yade and I am trying to simulate a cohesive material consists of sand particles that are connected by some elastic material. I choose the CohfrictMat as material and Ip2_CohFrictMat_CohFrictMat_CohFrictPhys for bonding. The question is when I define the normal stiffness of bonding (or contact), it is calculated by [1] harmonic average like: 1/(E1.D1)+1/(E2.D2). It is reasonable when two particles are compacting to each other. But when the two particles are under tension stress and leave each other, the stiffness of bonding should have nothing to do with the modulus of particle self and it should only depend on the bonding material itself. Also the shear stiffness should be different. As we know[2] the tensile crack is one of the main mechanism of compression. So how to define the stiffness of tensile?

###############################################here is my code########################

from __future__ import division
from __future__ import print_function

from future import standard_library
standard_library.install_aliases()
import time, sys, os, copy
young=1e6,
poisson=.6,

sigmaT=3.5e6,
frictionAngle=atan(0.8),
epsCrackOnset=1e-4,
relDuctility=30,

dtSafety=.8,
damping=0.4,
strainRateTension=-1,
strainRateCompression=-.5,
setSpeeds=True,

specimenLength=.04,

# isotropic confinement (should be negative)
isoPrestress=0,
)

#alphaKr=30,alphaKtw=30,
#concreteId=O.materials.append(FrictMat(young=15e6,poisson=.4,frictionAngle=0,density=0,label='frictionlessWalls'))

sp.toSimulation()
bb=uniaxialTestFeatures()
negIds,posIds,axis,crossSectionArea=bb['negIds'],bb['posIds'],bb['axis'],bb['area']
O.dt=0.5*PWaveTimeStep()

O.engines=[
ForceResetter(),
InteractionLoop(
[Ig2_Sphere_Sphere_ScGeom6D()],
[Ip2_CohFrictMat_CohFrictMat_CohFrictPhys(setCohesionNow = True)],
#setCohesionNow = True,setCohesionOnNewContacts = True
[Law2_ScGeom6D_CohFrictPhys_CohesionMoment(useIncrementalForm=True),
Law2_ScGeom_FrictPhys_CundallStrack()],
),
NewtonIntegrator(damping=damping,label='damper'),
#CpmStateUpdater(realPeriod=.5),
UniaxialStrainer(strainRate=strainRateTension,axis=axis,asymmetry=0,posIds=posIds,negIds=negIds,crossSectionArea=crossSectionArea,blockDisplacements=False,blockRotations=False,setSpeeds=setSpeeds,label='strainer'),
#PyRunner(realPeriod=4,command='stopIfDamaged()',label='damageChecker'),
#
]
plot.plots={'eps':('sigma',)}

plot.plot(subPlots=False)

O.timingEnabled=False

O.run()
################

Best regards,
Aaron

[2] Potyondy, D. O., & Cundall, P. A. (2004). A bonded-particle model for rock. International journal of rock mechanics and mining sciences, 41(8), 1329-1364.

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Jan Stránský
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Last query:
 Revision history for this message Jan Stránský (honzik) said on 2020-11-27: #1

Hello,

> I am a new user of Yade

welcome :-)

> But when the two particles are under tension stress and leave each other, the stiffness of bonding should have nothing to do with the modulus of particle self and it should only depend on the bonding material itself.

One way how to represent DEM is that particles are perfectly rigid and "their material" actually is (or defines) the properties of interactions (the bonding material).
From this point of view, yes, "the stiffness of bonding DO have nothing to do with the modulus of particle self and it DOES only depend on the bonding material itself".

However, for simple models, the stiffness of compression and tension equals, which is just from the definition of elastic material.
If you need different behavior, you have to use some more fancy material model.

Also note that in Yade changing of materials of particles has no effect on existing interactions.
On scenario for these use cases is:
- define materials of particles just for initial bonding
- create initial bonding
- change material of particles to "self" material (bonding interactions remain untouched), for the case of particle interactions after debonding / interactions of initially not bonded particles

> Also the shear stiffness should be different.

you are already using "poisson", which defines the "difference" of normal and shear stiffness [1].

cheers
Jan

 Revision history for this message Aaron Liu (voyagening) said on 2020-11-28: #2

Hi Jan,

>However, for simple models, the stiffness of compression and tension equals, which is just from the definition of elastic material.
If you need different behavior, you have to use some more fancy material models.

Does it mean that the whole material is made of the same material? I was wondering that when the mechanical properties(Elastic modulus and strength) of bonding material is distinct from particle material, like assume the bonding material is very soft and particles are tough, what material model and the physical module would be better satisfied?

Cheers,
Aaron

 Revision history for this message Jan Stránský (honzik) said on 2020-11-28: #3

> Does it mean that the whole material is made of the same material?

this is one (bot not the only one) approach

> what material model and the physical module would be better satisfied?

"something between" probably.
Concerning modulus, the best value is such that your overall/macroscopic modulus match the experiment/expectation.
Concerning strength, it is a bit more tricky. But similarly, some macroscopic response (strength, failure mode etc.) should match experiment/expectation.

cheers
Jan

 Revision history for this message Aaron Liu (voyagening) said on 2020-11-29: #4

Jan, Thank u so much.

 Revision history for this message Aaron Liu (voyagening) said on 2020-11-29: #5

Thanks Jan Stránský, that solved my question.

 Revision history for this message Bruno Chareyre (bruno-chareyre) said on 2020-12-15: #6

Hi,
A short comment related to this:
> But when the two particles are under tension stress and leave each other, the stiffness of bonding should have nothing to do with the modulus of particle self and it should only depend on the bonding material itself.

I can see where you come from: there is another material in between the particles with its own properties.
However, even in that case there is no reason to expect something different in traction and compression. If there is a cement paste in between, then it plays the same role in traction and compression (in elasticity at least).

Bruno

 Revision history for this message Aaron Liu (voyagening) said on 2020-12-24: #7

Hi Bruno,

I think u are right. But I would like to have a model that two hard particles are in contact with each other and another soft bonding material spread in the interspace. for example, you have a box of glass beads compacted well and then inject glue into gaps until it fulfills all the space. So in this case, when two particles are in compression, the stiffness is mostly dependent on the stiffness of the particle itself. cause they are in contact and soft bonding material could be ignored. But when you pull them away from each other, the bonding material should play the key role of stiffness.

Best,
Aaron