Dear Alireza Jafari,

   In structural analysis two types of damping can be specified, namely (1) Viscuous damping and (2) Structural damping (also referred to as material or hysteristic damping). 

Viscuous damping is defined wrt to the coefficient c such that damping force = c*(dy/dt). Damping ratio ζ is another means of specifying viscuous damping and and it is given by ζ  = c/ccr, that the ratio of actual damping to critical damping. The formula you gave for ζ is in order. Viscuous damping is frequency dependent.

Structural damping is defined by introducing a complex structural stiffness defined by K* = K(1+ i β) where i = sqrt(-1) and β = loss factor. In some literature β is written as 2β. Structural damping is frequency independent.

The response of a viscuously damped system is not exactly the same as that of a strucural damped system. The relationship between ζ and β is

             ζ  =   βωn/(2ω)

where ωn = natural frequency of a system and ω = frequency of the forcing function. Also, the viscuous damping coefficient c is related to the structural damping loss factor β by

                 c = βMωn2/ω 

Dear Alireza Jafari,

   In structural analysis two types of damping can be specified, namely (1) Viscuous damping and (2) Structural damping (also referred to as material or hysteristic damping). 

Viscuous damping is defined wrt to the coefficient c such that damping force = c*(dy/dt). Damping ratio ζ is another means of specifying viscuous damping and and it is given by ζ  = c/ccr, that the ratio of actual damping to critical damping. The formula you gave for ζ is in order. Viscuous damping is frequency dependent.

Structural damping is defined by introducing a complex structural stiffness defined by K* = K(1+ i β) where i = sqrt(-1) and β = loss factor. In some literature β is written as 2β. Structural damping is frequency independent.

The response of a viscuously damped system is not exactly the same as that of a strucural damped system. The relationship between ζ and β is

             ζ  =   βωn/(2ω)

where ωn = natural frequency of a system and ω = frequency of the forcing function. Also, the viscuous damping coefficient c is related to the structural damping loss factor β by

                 c = βMωn2/ω 

Hi

You cannot use modal damping well in SSI, at least not with absorbing boundary conditions. (https://www.researchgate.net/post/What_should_be_the_correct_boundary_condition_for_soil_when_accl-time_history_analysis_is_attempted_in_ABAQUS)

In Abaqus, you can use Rayleigh damping. This is unfortunatley not a very good damping model. See here, http://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.5/books/usb/default.htm?startat=pt04ch12s01abm40.html

If you have a wider interest in damping and phenomena confused with damping, perhaps you want to take a look here as well? http://qringtech.com/2014/06/22/designed-damping-types-mechanisms-application-limitation/

Sincerely

Claes

You should run a cyclc test (such as prescribing a sinusoidal strain history) considering the non-linear elasto-plastic constitutive law, then you look at the hysteresis loop for the stress-strain relationship and compute the area enclosed by the loop (dissipated work), W_D. You further compiute the elastic stored energy W_E considering the secant stiffness (this is one of the options) and then compute W_D/ W_E. This is proportional to the damping ratio. Please see the reference https://www.academia.edu/4479771/Nonlinear_modeling_of_carbon_nanotube_composites_dissipation_due_to_interfacial_stick_slip

if you want to use  damping ratio in ABAQUS , you should assign the values of two parameters of viscous damping , Alpha and Beta only........this means that your system will return to its position after oscillation as soon as possible. 

Recommendation:

Testing has shown that alpha (Alpha = 0.05 is the default) is the easier parameter to manipulate. Some general values and their effect are listed below:

Alpha=0.05

very little damping

Alpha=2.5

noticeable damping

Alpha=5-10

very noticeable damping

Alpha>10

pronounced damping and some difference between final deformed shapes obtained using different alpha values

hi, if i want to input critical damping=0.03 in abaqus what values of alpha ,beta , composite and structural should i consider in mechanical damping option of material property??