Rayleigh Damping
Rayleigh damping is described by two coefficients: the mass damping coefficient αdM and the stiffness damping coefficient βdK. Rayleigh damping will give the following contribution to the virtual work
Here P is the first Piola-Kirchhoff stress tensor.
Since Rayleigh damping is added directly to the virtual work equation, it does not affect the constitutive relation. As a consequence, the stresses and strains will for a linear elastic material still be in phase. This stands in contrast to the other damping models.
Rayleigh damping can be used both in the time domain and in the frequency domain.
Rayleigh damping is not directly related to any physical property. Historically, it was introduced since it was numerically attractive to have a damping matrix which was a linear combination of the mass and stiffness matrices
This operation is usually implied to be done at the global assembled matrix level. Such an interpretation is however only meaningful for pure structural mechanics problems, but not in a general multiphysics context. For this reason, Rayleigh damping in COMSOL Multiphysics is a material property, rather than a global property of the system of equations. If you enter the same Rayleigh damping parameters for all materials, and solve a pure structural mechanics problem, then the classical definition will be retrieved.