1. Reference problem

1.1. Geometry

The problem is axisymmetric (with axis \(Y\)). The punch consists of a single triangular element. It is assumed to be in initial contact with the massif at point \(A\), this point is therefore topologically confused between the punch and the massif.

1.2. Material properties

The block consists of an elasto-plastic material with linear isotropic work hardening:

\(E=\mathrm{2,0}\times {10}^{5}\mathrm{MPa}\)

\(\nu =\mathrm{0,3}\)

\({\sigma }_{y}=300\mathrm{MPa}\)

\({E}_{T}=5000\)

The punch is assumed to be rigid and is approximated by an elastic material with a large Young’s modulus:

\(E=\mathrm{2,0}\times {10}^{9}\mathrm{MPa}\)

\(\nu =\mathrm{0,3}\)

1.3. Boundary conditions and loads

The base of the massif is embedded and its left side is imposed at \(\mathrm{DX}=0\). Horizontal displacement is set to 0. The vertical displacement of the punch is imposed to \({u}_{A}=–\mathrm{0,4}\mathrm{mm}\), then increased by \(\mathrm{0,008}\mathrm{mm}\) (elastic return) according to the following graph: