The magnitude of stress is very small, <100 Pa. It can be ignored.
When the needle was pulled out, which boundary condition was used, Displacement or Velocity? Was the Boundary Condition applied to the entire body or on a selected face? If it was on a face, the BC introduced stress wave from the face and then the wave propagated into the body of the needle. This resulted in the stress you observed.
If the BC is applied to the entire body, you will observe very small or even zero stress in the needle.