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Re: [Question #668072]: Elastic modulus in Hertz-Mindlin contact

 

Question #668072 on Yade changed:
https://answers.launchpad.net/yade/+question/668072

Fu zuoguang posted a new comment:
Dear Prof. Chareyre and all users,

I now think my question can be answered by understanding that 'Young' in
H-M system in Yade is exactly refered to as elastic modulus and there is
always a transformation as G=E/[2*(1+v)] for its usage.

Some more about the H-M system are necessary to be summarized here. For
two spheres having the same material and radius,

(a)  the solution of the normal part of the contacting are provided by Hertz theory and the normal stiffness obeys
KN = (3*R_eq*G**2/(1-v)**2)**(1/3)*(F_n**(1/3));  (R_eq = 0.5*R)

(b)  the solution of the tangential part starts with a simplification that there is only no-slip occuring at the contact interface, so the tangential stiffness is only related to the normal one and is shown as
KT = 2*(1-v)/(2-v)*KN.

For testing, I picked out a contact from all in one case and then
recorded all needed parameters as

E=5.0e10(Pa)
v(Poisson's ratio)=0.2
R=1.0E-04(m)
F_n=1.89698e-2(N).

The calculation results are that 
KN=1.56858e5(N/m) and KT=1.39430e5(N/m)

These are the same as provided by Yade. So the Yade's calculation has no
question at all, whereas more details of especially the complex contact
model are suggested in the manual (Chapters 7)

Yours,
Zuoguang Fu

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