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, Layered Linear Elastic Material, Nonlinear Elastic Material, and Hyperelastic Material.

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, or Burgers. Then see the settings for each option that follows.

For some material models, you can select the shear modulus 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, hence they do not contribute to the stress. 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.

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

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 Linear 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 Maxwell enter the values for the parameter that describes the viscous behavior of the single dashpot connected in series with the spring.

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 in the parent Linear Elastic Material.

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

For linear viscoelasticity, in each Element row enter the stiffness of the spring 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, hence the dampers do not contribute to any stress. 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 given in the parent Linear Elastic Material.

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

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 order βv of the spring-pot. The default is 0.5 (dimensionless).

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

Note that the instantaneous stiffness is given in the parent Linear 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.

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

In the Shear modulus field, enter the stiffness of the spring Gv. The default is 2·1010 Pa.

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

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.

Note that the long-term stiffness is given in the parent Linear 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.

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

In the Shear modulus field, enter the stiffness of the second spring Gv2. The default is 2·1010 Pa.

When the Use fractional derivatives check box is selected, enter the fractional order βv1 and βv2 of the spring-pot pairs. The default is 0.5 (dimensionless) for both spring-pots.

Note that the instantaneous stiffness is given in the parent Linear Elastic Material.

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.

Uncheck 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 selected as one order less than what is used for the displacements. This results in that fewer extra degrees of freedom are 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, Layered Linear Elastic Material, Nonlinear Elastic Material, or Hyperelastic Material node selected in the model tree: