where βh is the coefficient of hygroscopic swelling, cmo is the moisture concentration, and cmo,ref is the strain-free reference concentration. It is possible to model bending due to a concentration gradient in the thickness direction of the shell.

Hygroscopic swelling can be modeled for the Linear Elastic Material, Layered Linear Elastic Material, and Layered Hyperelastic Material. The swelling can be applied to arbitrary layers in a multilayered shell when the Composite Materials Module analysis is available.

This section is present when this node is added under Layered Linear Elastic Material or Layered Hyperelastic Material node. In this section, select the layers in which hygroscopic swelling needs to be modeled.

If the Moisture concentration type differs between layers, you will need to add several Hygroscopic Swelling nodes with different layer selections. If only the material data values differ, you can use a single Hygroscopic Swelling node with From material. The data for each layer is then received from global Layered Material nodes.

For a multilayered shell, it is often easiest to add one Hygroscopic Swelling node per layer, if the temperature input is manual.

If the same layer is selected in two Hygroscopic Swelling nodes being active on the same boundary, the second definition will override the previous.

From the Concentration c list, select an existing concentration variable from another physics interface, if any concentration variables exist. For User defined enter a value or expression for the concentration. This is the midsurface concentration in the shell, controlling the membrane part of the hygroscopic swelling.

The unit for the input depends on the setting of Concentration type in the Hygroscopic Swelling Properties section. Only concentration variables having the chosen physical dimension are available in the Concentration list.

If needed, you can add a through-thickness concentration gradient in the Hygroscopic Bending section.

In the Concentration type list, select Molar concentration (the default) or Mass concentration, depending on the units used for the concentration.

Enter a Strain reference concentration cref. This is the concentration at which there are no strains due to hygroscopic swelling.

If Molar concentration is selected as Concentration type, also enter the Molar mass of the fluid, Mm. The default value is 0.018 kg/mol, which is the molar mass of water.

The default Coefficient of hygroscopic swelling βh uses values From material. For User defined select Isotropic (the default), Diagonal, or Symmetric to enter one or more components for a general coefficient of hygroscopic swelling tensor βh. The default value for the User defined case is 1.5e-4 m3/kg. When a nonisotropic coefficient of hygroscopic swelling is used, the axis orientations are given by the coordinate system selection in the parent node.

The Include moisture as added mass check box is selected by default. When selected, the mass of the fluid is included in a dynamic analysis, and when using mass proportional loads. It will also contribute when computing mass properties.

Enter the Concentration difference in thickness direction Δcz. This is the difference between the concentrations at the top and bottoms surfaces.

From the list, select Concentration difference in thickness direction or Concentration gradient in thickness direction.

When Concentration difference in thickness direction is selected, enter the concentration difference Δcz between the top surface of the topmost of the selected layers and bottom surface of the bottommost of the selected layers.

When Concentration gradient in thickness direction is selected, enter the concentration gradient c’ in the direction from the bottom surface to the top surface.

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