# deformation-dependent damping

As we know, if the damping model only depends on the instantaneous velocity, it can be called viscous damping, for which the damping force $f = Cv$. However, if $C$ depends on the deformation as $C(u),$ is this still named viscous damping? And if the damping force is modeled as $f=C g(v),$ where $g$ is a function of $v$, do we call this nonlinear viscous damping? Thank you!

A damping force like of the $f = Cg(v)$ could model something like frictional damping, where for example $C$ was a (negative) constant and $g(v) = v/|v|$, (i.e. for linear motion $g(v) = \pm 1$ depending on the direction of the motion) but calling it "nonlinear viscous damping" instead of "friction damping" seems rather pointless.