here, D is the diffusion coefficient in the reference configuration, and d represents the diffusion coefficient in the deformed configuration. The variables F and J are the deformation gradient and its determinant.

A constant diffusion coefficient D given in material frame implies that its corresponding value in spatial frame, d, depends on the deformation

The frame in which the diffusion coefficient is given can be specified in the Advanced section. From the Frame list select Reference configuration or Deformed configuration to specify a material or spatial diffusion.

The source term is a scalar quantity that is given per unit volume, so the same considerations apply as with the dependent variables, see Dependent Variables. The frame in which the source is given can be selected in the Advanced section.

here, Γ is the flux in the undeformed configuration, γ is the flux in the deformed configuration, F is the deformation gradient, and J is its determinant.

The External Flux node in the Transport in Solids interface allows adding additional domain fluxes. The frame in which the domain flux is given can be selected in the Advanced section.

Here, N is the normal to the undeformed boundary, n is the normal to the deformed boundary, and the variable JA is the ratio between the deformed area and the reference area. By default, the normal flux γn is set to the deformed configuration (spatial frame), but it is also possible to specify the normal flux in the reference configuration (material frame), Γn. The frame in which the normal flux is given can be specify in the Advanced section.