Viscous Damping Theory
Viscous damping can be added to the material models. It will cause an extra stress
S
q
proportional to the rate of elastic strain in the material,
where
η
b
and
η
v
are the bulk and shear viscosity coefficients, respectively.
Viscous damping can be used in both frequency and time domain analyses.
In case of geometric nonlinearity, the viscous stress is treated as being a Cauchy stress acting in the actual configuration (spatial frame). The resulting contribution to the second Piola–Kirchhoff stress is calculated as
where
is the inverse of the elastic Cauchy–Green tensor, and
J
el
is the elastic volume ratio.
is the inverse of the elastic Cauchy–Green tensor, and