When used together with Linear Elastic Material, Nonlinear Elastic Material, or Hyperelastic Material it is possible to model thermal expansion in the fibers. The assumption is that the volume of fibers is small when compared to the base material, and that thermal expansion (or contraction) occurs in the fiber direction only.

For Holzapfel–Gasser–Ogden and User defined fibers under Hyperelastic Material, the thermal expansion subfeature is disabled when the check box Contribute to total stress is selected.

The Volume reference temperature Tref is the temperature at which there are no thermal strains in the fibers. As a default, the value is obtained from a Common model input. You can also select User defined to enter a value or expression for the temperature locally.

The fiber Temperature T is by default obtained from a Common model input. You can also select an existing temperature variable from a heat transfer interface, if any temperature variables exist, or manually enter a value or expression by selecting User defined.

The settings in this section depend slightly on whether the parent Fiber node is a domain feature or a boundary feature.

From the Material list, select the Domain material or any other material to define the fiber’s thermal expansion properties. In most cases, you would use the domain material for the base material, and additional Material nodes without domain selection as the fiber material.

From the Material list, select the Boundary material or any other material to define the fiber’s thermal expansion properties. In most cases, you would use the boundary material for the base material, and additional Material nodes without domain selection as the fiber material.

Select an Input type to specify how the thermal strains in the fibers should be modeled. The default is Secant coefficient of thermal expansion, in which case the thermal strain in the fibers is given by

Here, the secant coefficient of thermal expansion α can be temperature-dependent.

When Input type is Tangent coefficient of thermal expansion, the thermal strain in the fibers is given by

where αt is the tangential coefficient of thermal expansion.

When Input type is Thermal strain, enter explicitly the thermal strain in the fibers dL as function of temperature.

In all three cases, the default is to take values From material. When entering data as User defined, enter the coefficient of the thermal expansion or the thermal strain in the fiber direction a, since thermal expansion is considered in the fiber direction only.

In all cases, the contribution to the thermal strain tensor is defined from the thermal strain in the fibers εth,fib, and the fiber direction a as

Physics tab with Fiber node selected in the model tree: