Forget what I said about my ASCE paper. I double-checked : the definition of timestep is detailed but damping is not (I though both were).
  Δaᵢ=-λaᵢsgn(Fᵢvᵢ'),   (**)

where vᵢ'=(vᵢ+½(aᵢΔt)), approximate of velocity between this and next
timestep.

Last remark : using v' as defined above, and not just "v" in the damping equation, can't probably be found in any paper. I introduced that after some tests in 1D, and found that it was better for high values of the timestep. More precisely, for cases where the sign of the velocity is reverted at each time-step, so you can't really tell if the force is opposed to it or not if you don't define (F,V) for the exact same time.

Bruno



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