The whole advanced oxidation model is based on a few main equations. The first one describes the oxidant diffusion

and the next equation treats the dynamics of with

as described in Section 3.2.1 and Section 3.2.2, respectively.

Because of the diffuse interface concept the volume increase of the generating oxide occurs only successively and not abruptly. As explained in Section 3.2.3, the volume increase of the oxidized material is calculated with the and values. After a time the normalized additional volume is determined by

The normalized additional volume directly loads the mechanical problem

because the principal axis components of the residual strain tensor are linearly proportional to in the form

The introduced so-called effective shear modulus in (see Section 3.2.5.2) can handle elastic and visco-elastic materials.

Ch. Hollauer: Modeling of Thermal Oxidation and Stress Effects