A small amount of high frequency damping is applied by default in the mechanical field; i.e. using a algorithm similar to the shock-wave smoothing algorithms used in hydrocodes.    In quasi-static problems, however, it can be advantageous to apply additional damping to gradually diminish the dynamic response of the system.  This can be achieved by defining *DAMPING, TYPE=PERCENTAGE Keyword by which a percentage damping is defined  based on an estimated value of the lowest vibration frequency computed using the Rayleigh quotient.  Generally percentage damping is specified in the range 0.01 - 0.03 (1% - 3%) as larger values of damping may result in significant over-damping which is generally detrimental to the solution.  In this case Damping_global_data is used to apply 2% percentage damping to the complete domain.

 

 

 

The equivalent ParaGeo data structure generated is Damping_global_data

 

The results are visualized by plotting the high definition history data for global energy and points output in files mech_001_2d_Case1d_000.hdh and mech_001_2d_Case1d_001.hdh respectively.

 

The time history for displacement and stress show that damping reduces the peak magnitude of the oscillations and eventually eliminates the dynamic response leading to a quasi-static stress state.  In achieving this state, however, there is still a small overshoot in stress at time t=1.0.   In an elastic simulation this is not significant.  In a nonlinear simulation, however, this could lead to a small additional non-recoverable deformation and is therefore not desirable.

Damping of the dynamic response is also evident in the time history of elastic energy.