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[loiseaurare <question630468@xxxxxxxxxxxxxxxxxxxxx>]

New question #630468 on Yade:
https://answers.launchpad.net/yade/+question/630468

Hi everybody, 

I have been browsing through the description of different cohesive contact laws, and I am now trying to understand the differences between JCFpmMat, CPMMat and cohFrictMat.

My question is on the formulation on the contact normal stiffness Kn, 

I read in the JcfPMMat and CPMMat description that this is defined by the function kn = 2*EcRaRB/(Ra+Rb)
Ec being the "Young modulus" parameter introduced in each of those contact laws, that actually does NOT define macroscopical youngs modulus. Ra and Rb being the radiuses of the two interacting particles.

In Dr Smilauer thesis, this formulation is introduced in a more general way, stating that kn in the algorithm is computed with the formula :

kn = k1k2/(K1 + K2)  => kn = E1l1~*E2l2~/(E1l1~+E2l2~) . Assuming that E1 and E2 are the same between the two particles, this yields

kn = E(l1~*l2~)/(l1~+l2~)

It is then precised in the thesis that for 'The most used class computing interaction properties Ip2_FrictMat_FrictMat_FrictPhys uses  ̃ l i~= 2ri. "

I think that Cohfrictmat and JcfPMat also use this formulation, am I correct ?

Then the concept of the equivalent cross section is introduced, as being another way to define the li~ length.

"Some formulations define an equivalent cross-section A eq , which in that case appears in the  li~ term 
as Ki = E i  * l i~ = Ei Aeq/li . Such is the case for the concrete model (Ip2_CpmMat_CpmMat_CpmPhys)
described later, where A eq = min(r 1 , r 2 ) "

And that is where I get lost. I do not understand the dimension of this Aeq over li quantity. I think that in the way it is expressed here, it actually has no dimension, where it should have a m dimension ?

If anybody can give a hint, I will appreciate ! 
Thanks in advance,
Manon


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