>> Your spheres have some microscopic young's moduli, but due to the >> disctribution of interactions you get macroscopic modulus that can be >> different; and I want to compensate that). I want to make sure that >> given a plane, sum of "surfaces" of all interactions (cylinders between >> spheres with the radius of the smaller sphere, right?) is equal to >> nominal, macroscopic surface of specimen. It depends on sphere radii >> discribution, for sure; perhaps it can be calculated analytically for >> regular arrangements. For other cases, the simulated rigidity may be >> artificially higher/lower. I haven't tried to quantify that yes, though. >> > > > If I understand what you mean, you want to compute analytically the > macroscopic young modulus as a function of the microscopic young > modulus. I am not sure there is currently a general way to do that for > random assembly, it is not easy at all. There were formula like that in > SDEC: the input was a macroscopic young modulus and SDEC computed > automatically the microscopic young modulus attributed to each > particles. But in reality it didn't work, the macroscopic young modulus > wanted was not reached. > The formula used were based on a paper from Cambou, but the formula, I > think, were valid only for a given fabric corresponding to the ones > studied by Cambou. > You can find more details in the PhD thesis of Sebastien Hentz who used > all that to simulate concrete with SDEC (in which there was a radius of > interaction greater than 1). In addition maybe you will find help about > interaction laws to use etc... in this thesis, unless you have already > read it. > > Yes, I have read it, thanks. I don't want to derive that analytically, I will plug intput and output into a neural network and train it to give me right interaction radius to have the same microscopic and macroscopic modulus (maybe, it is in collaboration) for different distributions - in some very primitive way at the beginning, though.
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