Use the Viscoelasticity 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 Linear Elastic Material, Nonlinear Elastic Material, Hyperelastic Material, Layered Linear Elastic Material, and Layered Hyperelastic Material.

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

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 — None, Williams-Landel-Ferry, Arrhenius, Tool-Narayanaswamy-Moynihan, or User defined.

Select a Material model — Generalized Maxwell, Generalized Kelvin-Voigt, Maxwell, Kelvin-Voigt, Standard linear solid, Burgers, or User defined. Then, enter the settings for each option that follows.

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

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

For Generalized Maxwell 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 Viscoelastic strains list, for each Branch row enter the stiffness of the spring Km in the Bulk modulus (Pa) column and/or Gm in the Shear modulus (Pa) column, and the relaxation time constant τm in the Relaxation time (s) column for the spring-dashpot pair in branch m.

When the Use fractional derivatives check box is selected, enter the fractional order βm in the Fractional order (1) column for each spring-spring-pot branch.

For large strain viscoelasticity, in each Branch row enter the energy factor of the branch, βvm, in the Energy factor (1) column and the relaxation time constant τm in the Relaxation time (s) column for the spring-dashpot pair.

When the check box Prune viscoelastic branches is selected, enter the Cutoff frequencies 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, deselected the check box, since 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 Prune viscoelastic branches is selected.

Select the Stiffness used in stationary studies, either Long-term or Instantaneous. With Long-term 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 (e.g. Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material). With Instantaneous all dampers are assumed to be rigid, and the material stiffness is given by springs arranged in parallel.

For Generalized Kelvin-Voigt 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 Viscoelastic strains list, for each Branch row enter the stiffness of the spring Km in the column labeled Bulk modulus (Pa) and/or Gm in the column labeled Shear modulus (Pa), and the relaxation time τm in the column labeled Relaxation time (s) for the spring-dashpot pair in the element m.

When the Use fractional derivatives check box is selected, enter the fractional order βm in the Fractional order (1) column for each spring-spring-pot branch.

Select the Stiffness used in stationary studies, either Long-term or Instantaneous. With Long-term all dampers are assumed to be relaxed. The material stiffness is therefore given by springs arranged in series. With Instantaneous 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 (e.g. Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

For Maxwell 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 Viscoelastic strains list, the relaxation time or viscosity is applied to the volumetric, deviatoric, or both volumetric and deviatoric deformation. Select an option from the Relaxation data list and edit the default as needed:

When the Use fractional derivatives 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 (e.g. Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

For Kelvin-Voigt 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 Viscoelastic strains list, the relaxation time or viscosity is applied to the volumetric, deviatoric, or both volumetric and deviatoric deformation. Select an option from the Relaxation data list and edit the default as needed:

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

When the Use fractional derivatives 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 (e.g. Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

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

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

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

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

When the Use fractional derivatives 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 (e.g. Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

For Burgers 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 Viscoelastic strains list, enter the Bulk modulus and/or the Shear modulus of the second spring in the Kv2 and Gv2 fields. The default values are 20 GPa.

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

When the Use fractional derivatives 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 (e.g. Linear Elastic Material, Nonlinear Elastic Material or Hyperelastic Material).

When Volumetric is selected from the Viscoelastic strains list, specify the Storage and loss moduli K' and K'', the Storage and loss compliances Q' and Q'', or the Loss factor ηv that defines the complex–valued bulk modulus.

When Deviatoric is selected from the Viscoelastic strains list, specify the Storage and loss moduli G' and G'', the Storage and loss compliances J' and J'', or the Loss factor ηv that defines the complex–valued shear modulus.

When Volumetric and deviatoric is selected from the Viscoelastic strains list, specify the Storage and loss moduli K', K'', G' and G'', the Storage and loss compliances Q', Q'', J' and J'', or the Loss factor ηv that defines the complex–valued bulk and shear moduli.

To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.

The check box Use local time integration is selected by default. Deselect 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 Use local time integration check box to select the Shape function type — Discontinuous Lagrange (default) or Gauss point data 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 Gauss point data.

Physics tab with Linear Elastic Material, Nonlinear Elastic Material, Hyperelastic Material, Layered Linear Elastic Material, Layered Hyperelastic Material node selected in the model tree: