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[Fu zuoguang <question232953@xxxxxxxxxxxxxxxxxxxxx>]

Question #232953 on Yade changed:
https://answers.launchpad.net/yade/+question/232953

    Status: Answered => Open

Fu zuoguang is still having a problem:
Dear Bruno Chareyre and all users:
     Thanks for helping me last time and I should say sorry for my absence of understanding what the rolling resistance really is. Hence I have spent just a week for getting a deep knowing about the special contact model that contains the rolling resistance parameters with the help of the article “A novel discrete model for granular material incorporating rolling resistance” from Jiang and the whole comprehension in my mind about this model can be expressed as 3 steps below:
    (1).The first and the most, it should be obviously known that the complete mechanical contact model is composed of normal, tangential and rolling contact components and rolling resistance can do affect the normal motion and the angular motion but not the translational motions of particles. “Law2_ScGeom6D_CohFrictPhys_CohesionMoment, which is elastic-plastic on moments in yade” I think that that contact law has nothing different from what I just said above. Is this right?
    (2).constitute a normal micro-mechanical rolling resistance model. That can be illustrated in the Fig1 below: 
    Each normal basic element includes a spring with stiffness as kn reflecting an elastic behavior, a dashpot with damping parameter allowing energy dissipation, and a divider to simulate the fact that traction force is not transmitted through a basic element at a point where the particles are not in contact at that point. There are just 3 steps for establishing this model: the first step is to consider the case that none of the dividers are separated, which we shall see corresponds to linear elastic case; the second is to turn to the case that some dividers are separated, which we shall associate with the plastic case and the last is to establish simplified rolling resistance models.
     At the first step, considering a contact where none of dividers are separated (Fig2), the moment M caused by rolling resistance is only relative to (called relative particle rotation here) and can be expressed as Eq.(1), where the Km is the rolling the stiffness here. This equation indicates that M increases linearly with relative particle rotation with the constant of proportionality Km.
     At the second step, considering a contact in which some dividers are separated (Fig3). With a fixed Fn, separation first occurs at the divider of the basic element at the right-hand edge of the contact and it should move continuously inward from the right-hand edge with the relative particle rotation increasing. A p is employed for described the contact force per unit length, the pmin in the right-hand edge and the pmax in the left-hand edge can directly calculated by Eq(2). Hence, M and Fn at the contact can then be obtained as Eq(3) ~ Eq(6).
     Finally, the whole rolling resistance may consist of an initial linear part and an non-linear part and the two idealized rolling contact models are introduced here for reducing the difficulties caused by nonlinearity, which can be shown as Eq(7).
     (3). Deriving the governing equations with rolling resistance based on local equilibrium conditions.
At the first step, a reduced problem can be determined, in which a particle is in contact with a wall and there is only a normal contact existing. Some important details about this reduced case are just in Fig4 and the whole processing of establishing equations for governing motions of particle with rolling resistance is expressed as that:
         1. The damping force of the Newtonian dashpot, which is taken as positive in positive X axis, is velocity-dependent and calculated by Eq(8).
         2. The total force by the normal contact, resulting from both the spring and the dashpot at this instant, can be calculated as Eq(9) and resultant force is as Eq(10).
         3. Based on Newton’s second law, the acceleration of the mass will then be obtained by Eq(11).
         4. Similarly, for angular motion, the moment due to the normal contact about the mass center at this instant, in which counter-clockwise rotation is positive, is obtained by Eq(12), and the resultant couple M can be calculated by Eq(13). Hence, the equation for angular motion can be expressed as Eq(14).
         5. After a series of format transformation, the governing equations with rolling resistance only for this reduced case can be described as Eq(15). The constant parameters in this equation are only relative to the shape and material attributes.
       At the second step, a particle with several contacts in a general case should be paid close attention to that a particle has lots of contacts with walls or other particles. The formats for this case can directly propagate from Eq(15) and can be expressed as Eq(16). So, all the works for establishing the governing equations with rolling resistance can be successfully finished at this stage.

After providing this very long expression, my question today are as that:
     (1) Are there something wrong in all my expressions above? If yes, please give me some suggestions for correcting them.
     (2).There is a very important detail that should be concerned about that there is only one part in rolling resistance model compared to standard DEM. It is just M(q). When this M(q) is fixed to zero, I think there is nothing different with standard DEM(Eq(17)). In yade, “Law2_ScGeom6D_CohFrictPhys_CohesionMoment” I think it can support this done, if yes, how can I do this?
      Seeking for your help!

Fig1: http://i.imgur.com/U2XJGNk.jpg

Fig2: http://i.imgur.com/oMlU1Mh.jpg

Fig3: http://i.imgur.com/W17OCEX.jpg

Fig4: http://i.imgur.com/ogZYqLA.jpg

Eq(1)-Eq(7): http://i.imgur.com/8sifMXr.jpg

Eq(8)-Eq(17): http://i.imgur.com/YQaYXzs.jpg

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