1. Reference problem

1.1. Geometry

Figure 1.1-1: Reference geometry

1.2. Material properties

The material obeys a law of behavior in large plastic deformations with linear isotropic work hardening.

The tensile curve is given in the plane logarithmic deformation - rational stress.

\(\sigma \mathrm{=}\frac{F}{S}\mathrm{=}\frac{F}{{S}_{0}}\mathrm{.}\frac{l}{{l}_{0}}\)
Figure 1.2-1: Tensile Curve	\(\begin{array}{c}\nu \mathrm{=}\mathrm{0,3}\\ E\mathrm{=}\mathrm{200000MPa}\\ {E}_{T}\mathrm{=}\mathrm{2000MPa}\\ {\sigma }_{y}\mathrm{=}\mathrm{1000MPa}\end{array}\)

\({l}_{0}\) and \(l\) are, respectively, the initial length and the current length of the useful part of the test piece.

\({S}_{0}\) and \(S\) are, respectively, the initial and current surfaces.

1.3. Boundary conditions and loads

The bar, of initial length \({l}_{0}\), locked in the direction \(Ox\) on the face [1,2] has a mechanical traction movement \({u}^{\mathit{meca}}\) varying linearly in time on the face \(\mathrm{[}\mathrm{3,}4\mathrm{]}\):

Figure 1.3-1: Limit conditions and loading