1. Reference problem

The problem is detailed in reference [1], in particular the loading path. Only a brief description of its main characteristics is presented here. Precision now that only the elastoplastic branch of behavior model KICHENIN_NL is mobilized; the viscoelastic branch is canceled by the introduction of a zero Young’s modulus \({E}^{v}\). The validation of this second branch is carried out in [V6.04.267]. Since the two branches are parallel, there is no coupling other than the sum of the constraints and the tangent operators, which justifies this validation choice. In this case, the model is reduced to an elastoplastic law with linear kinematic work hardening, completely similar to model VMIS_CINE_LINE; the latter will then serve as a reference.

1.1. Geometry

This is a « hardware point » test. It relies on the SIMU_POINT_MAT command.

1.2. Material properties

The material obeys the KICHENIN_NLavec law of behavior as characteristics:

\({E}^{p}=400\text{MPa}\)	Young’s modulus of the plastic branch
\({\mathrm{\nu }}^{p}=0.40\)	Poisson’s ratio in the plastic industry
\({\sigma }^{c}=8\text{MPa}\)	Elastic limit
\(C=80\text{MPa}\)	Prager constant
\({E}^{v}=0\)	Cancellation of the viscoelastic branch

1.3. Boundary conditions and loads

It is a load of imposed stresses of the Lissajous curve type, which is based on two directions (with orthogonal deviators) of stress \({\sigma }^{1}\) and \({\sigma }^{2}\). Based on \(\overline{t}\), the loading chronology is worth:

\(\sigma (\overline{t})={\sigma }^{c}\left[\mathrm{sin}(2\pi \overline{t}){\sigma }^{1}+\mathrm{sin}(4\pi \overline{t}){\sigma }^{2}\right]\) \(0\le \overline{t}\le 1\)

\({\sigma }^{1}=\left[\begin{array}{ccc}2.0& 0.0& 0.0\\ 0.0& 1.0& 0.0\\ 0.0& 0.0& 1.0\end{array}\right]\text{}\) \({\sigma }^{2}=\frac{\sqrt{2}}{3}\left[\begin{array}{ccc}0.0& 1.0& 0.5\\ 1.0& 0.0& 0.5\\ 0.5& 0.5& 0.0\end{array}\right]\text{}\)

1.4. Initial conditions

The system is considered to be in its natural state at \(t=0\). In particular, the plastic deformation is zero.