An ABAQUS/Explicit model often includes energy dissipation mechanisms—dashpots, inelastic material behavior, and the like—as part of the basic model. In such cases there is usually no need to introduce additional “structural” or general damping, as such damping would be unimportant compared to these other dissipative effects. However, some models do not have such energy dissipation sources, and some models require additional energy dissipation beyond that provided by other parts of the model. In such cases material damping may be desirable. Material damping is also discussed in “Material damping,” Section 3.6.3.
Material damping in ABAQUS/Explicit is Rayleigh damping, which is defined using the *DAMPING option, a suboption of the *MATERIAL option block. There are two damping factors associated with Rayleigh damping: 
for mass proportional damping and 
for stiffness proportional damping. Generally, mass proportional damping is used to damp out the low-frequency response, and stiffness proportional damping is used to damp out the high-frequency response (to smooth a noisy solution).
Mass proportional damping
The factor defines a damping contribution proportional to the mass matrix for an element. The damping forces that are introduced are caused by the absolute velocities of nodes in the model. The resulting effect can be likened to the model moving through a viscous “ether” so that any motion of any point in the model triggers damping forces.
Stiffness proportional damping
The factor defines damping proportional to the elastic material stiffness. A “damping stress,” 
, proportional to the total strain rate is introduced, using the following formula:
is the strain rate. For hyperelastic and hyperfoam materials 
is defined as the initial elastic stiffness. For all other materials is the material's current elastic stiffness. This damping stress is added to the stress caused by the constitutive response at the integration point when the dynamic equilibrium equations are formed, but it is not included in the stress output. Damping can be introduced for any nonlinear case and provides standard Rayleigh damping for linear cases. For a linear case stiffness proportional damping is exactly the same as defining a damping matrix equal to times the stiffness matrix. To avoid a dramatic drop in the stable time increment, the stiffness proportional damping factor, , should be less than or of the same order of magnitude as the initial stable time increment without damping.