2. Reference solutions

2.1. Isotropic plastic behavior

The reference solution is calculated analytically.

We note

the temperature, the plastic deformation, the cumulative plastic deformation and the total deformation at the moment of calculation, and

the same quantities at the previous moment. \({T}_{\mathrm{réf}}\) refers to the reference temperature.

The solution is calculated as follows:

This calculation is done in each direction. For the case being treated,

at any moment.

The constraint stored in Aster is the real constraint existing in each grid in this direction. The internal variables (

) are calculated from the equations above.

2.2. Kinematic plastic behavior

The reference solution is calculated analytically.

We note

the temperature, the plastic deformation and the kinematic work hardening variable at the time of calculation, and

the same quantities at the previous moment.

The solution is calculated as follows:

This calculation is done in each direction. For the case being treated,

at any moment.

The constraint stored in Aster is the real constraint existing in each grid in this direction.

2.3. Pinto Ménégotto behavior

The reference solution is that obtained by an Aster calculation with the same mesh on which charge/discharge cycles are applied, in imposed displacement, making it possible to recreate the deformations resulting from the thermo-mechanical calculations presented below. The corresponding test is therefore only a non-regression test, by comparing the constraints obtained by these two types of modeling: on the one hand mechanical, and on the other hand thermo-mechanical.

The constraint stored in Aster is the real constraint existing in each grid in this direction.