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During the first phase of a design accident of type APRP (Primary Refrigerant Loss Accident), fuel rods are subject to a rapid rise in temperature, to phase transformations of the material and to changes in conditions at mechanical limits. The study of a APRP accident requires a good knowledge of the behavior of the fuel rod sheath during the first phase called "swelling-rupture". In particular, it is necessary to have a good idea of the total deformation of the sheath.

Models of phase transition, mechanical behavior and rupture have been developed, and identified on the basis of experimental tests.

For the metallurgical part, Zircaloy undergoes metallurgical transformations between :math:`700°C` and :math:`1000°C`, where they pass from a compact hexagonal structure phase (alpha or :math:`\alpha` cold phase) to a cubic structure phase (beta or :math:`\beta` hot phase). We will find in [:ref:`R4.04.04 <R4.04.04>`], the equations governing the kinetics of transformations during heating (:math:`\alpha` turns into :math:`\beta`) and at cooling (:math:`\beta` turns into :math:`\alpha`).

For the mechanical part, the model is written in one dimension, in the circumferential direction of the tube. Even if this model is consistent with the experiments, its use to perform 3D finite element calculations is not possible. In addition, zirconium alloys have anisotropic behavior, at least in phase :math:`\alpha`, that cannot be taken into account in a 1D model. From a stress point of view, the tube undergoes an azimuthal temperature gradient causing circumferential, but also axial, deformation gradients, which it is important to take into account in order to obtain a response in accordance with the experiment.

This is why, department MMC has formulated a 3D model to describe the behavior of the Zircaloy sheath in the case of a APRP analysis. Norton's laws describing the 1D behavior of the material in various fields :math:`(\alpha ,\alpha \mathrm{-}\beta ,\beta )` are replaced by Lemaître's laws, taking into account the anisotropy of the :math:`\alpha` phase. Phase :math:`\beta` is isotropic. Domain :math:`\alpha \mathrm{-}\beta` is supposed to have anisotropy that is proportional to the rate of presence of phase :math:`\alpha`.

Here we describe the numerical implementation of this model, available in *code_aster* under the name META_LEMA_ANI, and its resolution algorithm. It is available in 3D, plane deformation, axisymmetry.