Type of damping to be selected for dynamic analysis

I am modeling a system with two steel bars (incident bar and transmission bar) and a rock sample in between. A incident pulse is applied on the left end of the incident bar. The pulse is shown below. The analysis is run for a very short duration 0.0011s. During this time, there is no loss of energy when the pulse travel through the bars i.e. damping is zero. When the pulse travels through the rock, due to joints there must be some loss of energy and hence damping must be given. My questions are

  1. What kind of damping can I specify : local damping or Rayleigh damping?
  2. I plotted the stress-xx history along various points of the bar i.e., left, center and right of the incident and transmission bar. At the left of the incident bar, I must get the same history as my input pulse which I am getting. I am also getting the same pulse at the center of IB. However, at the right of the incident pulse, the pulse has a higher peak. The stress-xx at the incident bar (right) must equilibrate with stress-xx at the transmission bar (left) so that the rock deforms under stress equilibrium. However, I am not sure why I cant get that. Is it due to different mesh size near the interfaces? Can someone help?
    Thank you.
    Fig 1 is the incident pulse applied. Fig 2 is the bar setup with rock in between. Fig 3 is closer view of the rock sample.

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