Damping can be introduced as a material property to account for dissipative mechanisms in dynamic analyses.
Contributions from the various material damping sources are additive. The contribution of material damping, in turn, is additive to the total structural damping. For a list of all available damping sources, see Damping Matrices in the Theory Reference.
The following material damping topics are available:
Material-dependent damping enables you to specify mass-proportional Rayleigh damping (alpha damping) or stiffness-proportional Rayleigh damping (beta damping) as a material property.
Rayleigh damping is widely used to provide an energy-dissipation mechanism when analyzing complex engineering structures responding to dynamic loads such as seismic ground motion.
For more information about Rayleigh damping, see Alpha and Beta Damping (Rayleigh Damping) in the Structural Analysis Guide.
Define material-dependent alpha and beta damping using either linear material property (MP) or data-table (TB) commands. Both methods have advantages, as follows:
If defining Rayleigh damping via MP and TB commands, the damping matrix is the sum of each source of damping, as shown in Equation 14–37.
4.26.1.1.1. Defining Rayleigh Damping via MP
Define mass-proportional Rayleigh damping via MP,ALPD, and stiffness-proportional Rayleigh damping via MP,BETD.
Rayleigh damping via MP commands defines the damping coefficients for the whole element, but not for each material in a multi-material element. For multi-material elements such as SOLID185 Layered Structural Solid, therefore, damping coefficients are determined from the material pointer for the element (MAT) rather than from the section materials.
Rayleigh damping defined via MP commands is not temperature-dependent and are always evaluated at T = 0.0.
To define Rayleigh damping, specify the damping option(s) and the constants (ALPD and/or BETD), as follows:
| Constant | Meaning | Property | Mechanical APDL Theory Reference Equation |
|---|---|---|---|
| ALPD |
| Mass-proportional material damping for material 
| Equation 14–37 |
| BETD |
| Stiffness-proportional material damping for material 
| Equation 14–37 |
Example 4.52: Defining Mass-Proportional Material Damping (MP,ALPD)
/prep7 ! Elastic properties and density mp,ex,1,2.0e11 mp,nuxy,1,0.2 mp,dens,1,7800 ! Mass proportional damping mp,alpd,1,50
You can define stiffness-proportional damping in a similar manner (MP,BETD).
4.26.1.1.2. Defining Rayleigh Damping via TB
The TB method for defining damping coefficients is suitable for multi-material elements requiring definition of damping coefficients for section materials. Define mass-proportional Rayleigh damping via TB,SDAMP,,,,ALPD, and stiffness-proportional Rayleigh damping via TB,SDAMP,,,,BETD. For a list of elements supporting this method, see Material Model Support for Elements.
The TB method is useful for modeling layered composite materials consisting of a damped layer sandwiched between non-damped layers. It is also a powerful way of defining Rayleigh damping when field-variable dependence is desired.
This damping feature also allows damping coefficients to be specified for the element as a whole, as occurs via Rayleigh-damping MP commands. If damping is uniform for the element with no field-variable dependence, however, consider using the corresponding MP commands. When damping is defined via TB commands, the damping matrices are integrated similar to the structural stiffness and mass matrices and may be more resource-intensive.
The stiffness-proportional damping matrix calculated when using TB,SDAMP,,,, BETD does not include the stress stiffening included in the structural stiffness due to nonlinear geometry (NLGEOM,ON). Stress stiffening is ignored in the damping matrix calculation as it is not a material property. To include stress-stiffening in the damping matrix calculation, use MP,BETD.
When defining Rayleigh damping via TB:
| Constant | Meaning | Property | Mechanical APDL Theory Reference Equation |
|---|---|---|---|
| C1 |
| Mass proportional material damping for material 
| Equation 14–37 |
| C1 |
| Stiffness proportional material damping for material 
| Equation 14–37 |
Both mass- and stiffness-proportional damping coefficients can be defined as frequency-, temperature-, or time-dependent properties (TBFIELD). Frequency-dependent properties are supported for full harmonic analyses only.
Example 4.53: Stiffness-Proportional Material Damping (TB,SDAMP,,,,BETD)
This example shows stiffness proportional damping as a function of temperature, with temperatures specified for each set of constants (TBFIELD,TEMP).
Define the section as a shell section (SECTYPE,,SHELL). Assign separate damping constants to the layers by defining different stiffness-proportional damping values for each of the layer materials (SECDATA). You can define mass proportional damping in a similar manner.
/prep7 ! Elastic properties and density mp,ex,1,2.0e11 ! Material 1 mp,nuxy,1,0.25 mp,dens,1,7800 mp,ex,2,2.2e11 ! Material 2 mp,nuxy,2,0.2 mp,dens,2,5800 ! Stiffness proportional damping TB,SDAMP,1,,,BETD ! Material 1 TBFIELD, TEMP, 10 ! Define first temperature TBDATA,,1.0e-3 TBFIELD, TEMP, 100 ! Define second temperature TBDATA,,5.0e-3 TB,SDAMP,2,,,BETD ! Material 2 TBFIELD, TEMP, 40 ! Define first temperature TBDATA,,2.0e-3 TBFIELD, TEMP, 100 ! Define second temperature TBDATA,,1.0e-3 ! Apply section specific damping sect,1,shell ! Specify shell section secd,0.1,1 ! Layer 1, Material 1 secd,0.1,2 ! Layer 2, Material 2 secd,0.1,1 ! Layer 3, Material 1
Material structural damping is a form of stiffness proportional
damping. This damping option allows you to specify the structural damping coefficient(s)
and/or 
for each material 
.
For more information, see Harmonic Analysis in the Structural Analysis Guide.
You can define material-dependent structural damping using either linear material property (MP) or data-table (TB) commands:
4.26.2.1. Using MP to Define Material-Dependent Structural Damping Coefficients
You can define the structural damping coefficient 
using MP,DMPS.
| Constant | Meaning | Property | Mechanical APDL Theory Reference Equation |
|---|---|---|---|
| DMPS |
| Structural damping coefficient for material 
| Equation 14–39 |
Example 4.54: Structural Damping (MP,DMPS)
/prep7
! Elastic properties and density
mp,ex,1,2.0e11
mp,nuxy,1,0.25
mp,dens,1,7800
! Structural damping
mp,dmps,1,0.1
4.26.2.2. Using TB to Define Material-Dependent Structural Damping Coefficients
You can define the structural damping coefficient 
using TB,SDAMP,,,,STRU.
Defining structural damping using this method specifies damping in terms of the loss factor, equal to twice the damping ratio at the resonance frequency.
For the relationship between different structural damping coefficients, see Comparing Structural Damping Coefficient Options .
Define the elastic behavior using the elasticity table (TB,ELASTIC), and density via the MP command. Initialize the material data table (TB,SDAMP,,,,STRU), and enter the appropriate damping coefficient (TBDATA).
| Constant | Meaning | Property | Mechanical APDL Theory Reference Equation |
|---|---|---|---|
| C1 |
| Structural damping coefficient for material
| Equation 14–39 |
For a full harmonic analysis, the structural damping coefficient can be frequency- or temperature-dependent (TBFIELD).
Example 4.55: Structural Damping (TB,SDAMP,,,,STRU)
/prep7 ! Elastic properties and density tb,elastic,1 tbdata,,2.0e11,0.25 mp,dens,1,7800 ! Structural damping tb,sdamp,1 ! TBOPT=STRU is the default tbdata,,0.2
The generalized Maxwell model consists of springs representing elastic stiffness and dashpots representing dissipative mechanisms inherent in viscoelastic materials. (See Figure 4.26: Generalized Maxwell Solid in One Dimension.) The Maxwell model is useful for modeling damping mechanisms in harmonic analyses.
In the harmonic domain, the Maxwell model consists of imaginary
components of the shear and bulk moduli (Equation 4–61), commonly referred
to as the loss moduli. The loss moduli are used to construct the viscoelastic damping matrix
(
in Equation 14–39). This is done by using the loss
moduli divided by frequency and subsequently forming the damping matrix in a manner similar to
the formation of the element stiffness matrix.
For more information, see Harmonic Viscoelasticity.