2. Principle of creep/plasticity coupling

The coupling is carried out during the internal resolution at the Gauss point in the framework of an iterative algorithm in which creep and plasticity calculations are chained.

To perform such coupling, a module is integrated into the local resolution of operators STAT_NON_LINEDYNA_NON_LINE a module allowing the resolution of creep and plasticity to be calculated successively from the same initial state (constraints and internal variables, deformations and deformation increments). The principle is as follows: when resolving at the Gauss point, starting from the initial state in terms of stresses, internal variables and deformations, a creep calculation is performed. The creep deformation increment calculated during the creep resolution is then deduced from the total deformation increment, and provided as an argument for the plasticity resolution. The plasticity is resolved, starting from the same initial state in terms of stresses, internal variables and deformations, except for the total deformation increment, from which the creep deformation increment has been removed. When the plastic deformation increment has been calculated, after resolving the plasticity, it is possible to correct the deformation value at the input of the creep calculation, and repeat the creep/plasticity chained calculation, until the convergence of the solution is obtained, that is to say the stability of the stresses and of the creep and plasticity deformations.

The stresses calculated using the creep equations are in principle not identical to those of the plasticity equations. Their equality is not formally written in the equations. But when the creep/plasticity balance is reached, it can be shown that the stresses at the exit of the creep are indeed equal to the stresses at the exit of the plasticity (see paragraph 3.2).

As the coupling is solved by chaining the resolutions of creep and plasticity during an iterative algorithm, this allowing a low computer development cost, the calculation of the tangent matrix is performed exclusively from the plasticity model, without taking into account creep or creep/plasticity coupling, for the sake of simplification. The creep deformations then constitute a loading for the plasticity calculation. This assumes that the evolution of creep is slower than the evolution of plasticity.

This simplification, which is all the more relevant as the calculation step is wisely chosen, makes it possible to converge towards the (global) solution with a slightly larger number of global iterations than in the case where the tangent matrix is calculated exactly, but does not alter the result of the calculation (converged) in any way.