| Thread Previous • Date Previous • Date Next • Thread Next |
Hi Jan, My two cents about symmetry of stress :
This definition of stress is assuming static equilibrium. In this situation, there is a mathematical proof that the result will be symmetric, even if it there is no obvious symmetry in the formula. IIRC, the proof is based on (1) the decomposition of branch into O1C-O2C, and (2) the fact that the total torque of all forces on one grain is 0. If we are not stricly at static equilibrium, this definition does not apply. DEM is never stricly at equlibrium, so this stress is never exactly symmetric, but it is usually very close.f*branch.transpose() R*T*n[i]*t[j]
If you do this :
you get something symmetric. Ok, it looks better, but you are in fact only hidding the initial mistake : abusing static equlibrium assumption, and the result in itself is not better. I'd keep the non-symmetric definition, and the non symmetry of the result would just remind people to be carefull with that. For dynamic cases, there are other definitions of stress, considering kinetic energy of grains, probably not what you want at the moment..5*(f*branch.transpose() + branch*f.transpose()) R*T*.5*(n[i]*t[j]+n[j]*t[i]) which is standard way of tensors symetrization.
Cheers. Bruno
| Thread Previous • Date Previous • Date Next • Thread Next |
