Yade

Elastic modulus in Hertz-Mindlin contact

Asked by Fu zuoguang

Dear Prof. Chareyre and all users,

The formulation of Hertz-Mindlin interaction in Yade is as implemented in PFC.
In PFC, The elastic modulus used in contact as two spheres touching each other is their
shear modulus, G_1 and G_2(or called equivalent shear modulus, G_eq), whereas in Yade, this
parameter for H-M type is still called as 'Young'(E_1 and E_2).

Does a transformation exist between the two as

G=E/[2*(1+v)],

or the 'Young' directly represents the shaer modulus?

Seeking your help!

Zuoguang Fu

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Bruno Chareyre
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Best Bruno Chareyre (bruno-chareyre) said : 		#1

Hi,
I don't know precisely, but the H-M in Yade also has a "Poisson" parameter...
I would suggest to check the code to be sure how they are converted.
HTH
Bruno

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Fu zuoguang (zgfu1985) said : 		#2

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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Fu zuoguang (zgfu1985) said : 		#3

Thanks Bruno Chareyre, that solved my question.

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Bruno Chareyre (bruno-chareyre) said : 		#4

Thx for feedback.
B