Hello Sega I'm not the author of those relations, but I'll do my best to clarify a little bit (is Frederic Donze around to give better explanations?).
"/therefore, in my opinion, the contact stiffness (kn, ks) and the viscous damping coefficients (cn,cs) should be calculated proceeding from the coefficient of restitution and duration of impact."/ There is no such damping coefficient in current contact laws. There is only a numerical damping, called "non-viscous damping" in Cundall's papers, which applies at the level of resultant forces and moments on each particle (see damping classes). > /I have found in the Annual Report 2006 of Discrete Element Group for Hazard > Mitigation, page E5 > (http://geo.hmg.inpg.fr/frederic/Discrete_Element_Group_FVD.html) expressions > for kn, ks: > > if > > E = D/S * Kn * ( beta + gamma * Ks/Kn ) / (alpha + Ks/Kn) > v = (1 - Ks/Kn) / (alpha + Ks/Kn)/ > Is it clear for you that in the equations above *E and v are elastic parameters of a sphere packing*, measured in a simulated test? I guess alpha, beta, gamma are ad-hoc coefficients that fit the curves obtained after a parametric study of E/kn =f(ks/kn) and v=f(ks/kn) in a simulated triaxial test (otherwise, i don't see how 3 coefficients can be computed from 2 equations!). Note that these relations probably depend on the compacity of the packing and particle size distribution. > /hence > > Kn = E * S/D * (1 + alpha) / [ beta * (1 + v) + gama * (1 - alpha*v) ] > Ks = Kn * (1 - alpha*v) / (1 + v)/ > Here, kn and ks are constants stiffness coefficients that WILL give you given values of macroscopic elastic moduli Em and vm. Hence, the model is not based on Eg, vg of the grains, it is based on Em, vm that you want to obtain at the scale of the packing. This is in fact a common situation when you want to simulate soil or concrete. > where alpha, beta, gamma is the parameters will be identified; E, v is > Young's > Modulus and Poisson ratio. > > However, I on former do not understand as they have turned out and how can be > used in the linear contact model > Fn = kn * xn, > Ft = kt * xt > where xn - depth penetration, xt - relative tangential displacement. > > I'm not sure I understand the problem. If constants kn and ks are defined, then you can compute the forces based on positions/displacement, there is nothing more here (note that second equation is in fact used in an incremental vectorial form : dFt = kt * dxt). > I'm interested to that I write the PhD thesis about modelling the granulated > materials in which there is a review of various models of interaction: linear > and nonlinear viscoelastic models (Cundall*Strack, Kuwabara&Kono), > Hertz theory, elastoplastic models (Walton&Braun, Thronton), linear and > nonlinear tangential interaction (Mindlin&Derisevich, Walton&Braun). > The model of interaction in ElasticContactLaw in Yade is linear elastic in normal direction, and linear elasto-plastic in tangential direction, exactly the same as in most Cundall's papers. The relations with alpha, beta, gamma is just a trick to choose the values of kn and ks. > In the linear models factors of elasticity and dissipation are deduced from > the decision of the differential equation of pair interaction and > __empirically__ defined parameters, such as coefficient of restitution and > duration of pair impact. In the nonlinear models constructed on the basis of > the theory of elasticity Hertz, the given parameters define on the basis of > __clearly interpreted physical parameters__ of a body: the Young's Modulus > and Poisson's ratio. > Again, to be sure it is clear : there is no dissipation at contact, and there is nothing like a restitution coefficient or a priori duration of impact in Yade, appart from the ones you can observe in the results of a simulation. There is just kn, ks, and numerically damped Newton's laws. I hope it helps. Bruno -- _______________ Chareyre Bruno Maitre de conference Institut National Polytechnique de Grenoble Laboratoire 3S (Soils Solids Structures) - bureau I08 BP 53 - 38041, Grenoble cedex 9 - France Tél : 33 4 76 82 52 76 Fax : 33 4 76 82 70 00 ________________ _______________________________________________ Yade-users mailing list [email protected] https://lists.berlios.de/mailman/listinfo/yade-users
