1. Reference problem

The problem is detailed in reference [1], in particular obtaining the analytical solution. Only a brief description of its main characteristics is presented here. Precision now that only the viscoelastic branch of behavior model KICHENIN_NL is mobilized; the elastoplastic branch is limited to elasticity by the introduction of a sufficiently high plasticity threshold. The validation of this second branch is carried out in [V6.04.268]. 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.

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 law of viscoelastic behavior KICHENIN_NLavec as characteristics:

\({E}^{p}=400\text{MPa}\)	Young’s modulus of the plastic branch
\({\mathrm{\nu }}^{p}=0.15\)	Poisson’s ratio in the plastic industry
\({E}^{v}=800\text{MPa}\)	Young’s modulus of the viscoelastic branch
\({\mathrm{\nu }}^{v}=0.3\)	Poisson’s ratio of the viscoelastic branch
\({\mathrm{\nu }}^{d}=0.25\)	Poisson’s ratio of the nonlinear shock absorber
\(n=0.5\)	Exponent of the nonlinear damper (\(\gamma =2\))
\(\eta =200{\text{MPa.s}}^{1/2}\)	Viscosity coefficient of the nonlinear shock absorber

1.3. Boundary conditions and loads

This is a loading of imposed constraints, the expression of which will be seen in §2.1. It is based on two parameters: a characteristic time \({t}_{c}\) which determines the loading speed and a stress load on the \({\sigma }^{0}\) shock absorber.

\({t}_{c}=2.5\text{s}\)	Typical load time
\({\sigma }^{0}=\frac{10}{\sqrt{1.87}}\left[\begin{array}{ccc}1.0& 0.1& 0.3\\ 0.1& 0.2& 0.5\\ 0.3& 0.5& 0.4\end{array}\right]\text{MPa}\)	Shock absorber stress (in MPa)

1.4. Initial conditions

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