Viscoelasticity

Use the subnode to add viscous stress contributions to an elastic material model. This material model is available in the Solid Mechanics, Shell, Layered Shell, and Membrane interfaces, and can be used together with , , , , and .

Note: Some options described below are only available with certain COMSOL products (see https://www.comsol.com/products/specifications/).

	See also Linear Viscoelasticity and Large Strain Viscoelasticity in the Structural Mechanics Theory chapter.

Viscoelastic models are often conceptually viewed as rheological networks consisting of spring and damper elements. The sketch section shows the arrangement of springs and dampers for the chosen viscoelastic material model. If fractional derivatives are enabled, the dampers are replaced by so-called spring-pot elements. Relevant input parameters are shown next to the spring, damper, and spring-pot elements. The elastic stiffness contribution of the parent material model is indicated by a light gray spring symbol representing the bulk and shear moduli, K and G, respectively.

Viscoelastic properties have a strong dependence on the temperature. For thermorheologically simple materials, a change in the temperature can be transformed directly into a change in the time scale. Thus, the relaxation time is modified to aT(T)τm, where aT(T) is a shift function.

Select a Shift function — , , , , or .

Select a — , , , , , , or . Then, enter the settings for each option that follows.

From the list select , , or . Select when the viscoelastic behavior applies only to the volumetric deformation. The option (default) applies the viscoelastic relaxation to the shear deformation only. With the viscoelastic strain is full.

For some material models, you can select the stiffness to use when solving a stationary problem. Select the — or . With all dampers are assumed to be fully relaxed, whereas with all dampers are assumed to be rigid.

For enter the values for the parameters that describe the viscoelastic behavior as a series of spring-dashpot pairs.

Depending on the selection done in the list, for each row enter the stiffness of the spring Km in the column and/or Gm in the column, and the relaxation time constant τm in the column for the spring-dashpot pair in branch m.

When the check box is selected, enter the fractional order βm in the column for each spring-spring-pot branch.

For large strain viscoelasticity, in each row enter the energy factor of the branch, βvm, in the column and the relaxation time constant τm in the column for the spring-dashpot pair.

When the check box is selected, enter the flower and fupper. The relaxation times τm are frozen and cannot be changed when the check box is selected. In order to change these settings again, clear the check box because pruning is only performed at the time when the check box is selected. It is also required that the relaxation times for each branch have constant values when is selected.

From the list, select either or . With , all dampers are assumed to be relaxed; hence the branches do not contribute to the stress. The material stiffness is therefore given by the stiffness in the parent material model (for example, Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material). With , all dampers are assumed to be rigid, and the material stiffness is given by springs arranged in parallel.

For enter the values for the parameters that describe the viscoelastic behavior of multiple Kelvin–Voigt elements arranged in series.

Depending on the selection done in the list, for each row enter the stiffness of the spring Km in the column labeled and/or Gm in the column labeled , and the relaxation time τm in the column labeled for the spring-dashpot pair in the element m.

When the check box is selected, enter the fractional order βm in the column for each spring-spring-pot branch.

Select the , either or . With , all dampers are assumed to be relaxed. The material stiffness is therefore given by springs arranged in series. With , all dampers are assumed to be rigid; hence the viscoelastic branches do not contribution to the strain, and the instantaneous stiffness is determined by the parent material only (for example, Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

For enter the parameters that describes the viscous behavior of a single dashpot connected in series with a spring.

Depending on the selection done in the list, the relaxation time or viscosity is applied to the volumetric, deviatoric, or both volumetric and deviatoric deformation. Select an option from the list and edit the default as needed:

When the check box is selected, enter the fractional order βv of the spring-pot. The default is 0.5 (dimensionless).

Note that the instantaneous stiffness is given by the parent material model (for example, Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

For enter the values for the parameter that describes the viscous behavior of the single dashpot in parallel with a spring.

Depending on the selection done in the list, the relaxation time or viscosity is applied to the volumetric, deviatoric, or both volumetric and deviatoric deformation. Select an option from the list and edit the default as needed:

For large strain viscoelasticity, enter the τv. The default is 3000 s.

When the check box is selected, enter the fractional order βv of the spring-pot. The default is 0.5 (dimensionless).

Note that the instantaneous stiffness is given by the parent material model (for example, Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

For enter the values for the parameters that describe the viscoelastic behavior of the single spring-dashpot branch.

Depending on the selection done in the list, enter the and/or the of the spring in the Kv and Gv fields. The default values are 20 GPa.

For linear viscoelasticity, select an option from the list and edit the default as needed:

For large strain viscoelasticity, enter the τv, which default value is 3000 s, and the βv of the dashpot. The default is 0.2.

When the check box is selected, enter the fractional order βv of the spring-pot. The default is 0.5 (dimensionless).

Note that the long-term stiffness is given by the parent material model (for example, Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

For enter the values for the parameter that describes the viscous behavior of the spring dashpot in series with a second spring-dashpot pair.

Depending on the selection done in the list, enter the and/or the of the second spring in the Kv2 and Gv2 fields. The default values are 20 GPa.

For linear viscoelasticity, select an option from the list and edit the default as needed:

When the check box is selected, enter the fractional orders, βv1 and βv2, of the spring-pot pairs. The default is 0.5 (dimensionless) for each spring-pot.

Note that the instantaneous stiffness is given by the parent material model (for example, Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

When is selected from the list, specify the K' and K'', the Q' and Q'', or the ηv that defines the complex–valued bulk modulus.

When is selected from the list, specify the G' and G'', the J' and J'', or the ηv that defines the complex–valued shear modulus.

When is selected from the list, specify the K', K'', G' and G'', the Q', Q'', J' and J'', or the ηv that defines the complex–valued bulk and shear moduli.

These expressions can be entered as functions taken directly from interpolated data, or can be analytical expressions of the frequency variable.

	The User defined viscoelastic models are applicable in Frequency Domain and Eigenfrequency study steps only. The internal variables for the frequency f and angular frequency ω are named phys.freq and phys.omega, respectively. Here, phys is the tag of the parent physics (for instance, solid).

To display this section, click the button (

) and select in the dialog box.

The check box is selected by default. Clear it in case you want to use the global time integration scheme. The check box is only available for the Generalized Maxwell and Standard Linear Solid models. For all other viscoelasticity models, the global time integration is used.

Clear the check box to select the — (default) or for the components of the auxiliary viscoelastic tensor. When the discontinuous Lagrange discretization is used, the shape function order is set as one order lower than the order used for the displacement field. This results fewer degrees of freedom being added to the model than when using Gauss point data. The accuracy does in general not differ much. If you want to enforce that the constitutive law is fulfilled at the integration points, select .

	To compute the energy dissipation caused by viscoelasticity, enable the Calculate dissipated energy check box in the Energy Dissipation section of the parent material node.

Physics tab with , , , , node selected in the model tree: