1. Reference problem

1.1. Geometry

1.2. Material properties

The material obeys Norton’s law of viscoplastic behavior (particular case of Lemaître’s law, where the parameter UN_SUR_M is zero, confer [R5.03.08]), whose parameters are:

• Young’s module: \(E=80000\mathit{MPa}\)

• Poisson’s ratio: \(\mathrm{\nu }=0.35\)

• \(n=4.39\)

• \(K=253.5497\mathit{MPa}\mathrm{.}{s}^{-1}\)

• \(\alpha =0.00004\)

1.3. Boundary conditions and loads

The bar, of initial length

, stuck in the direction

on the side [1,2] is subjected to a uniform temperature

and to a mechanical tensile displacement u on face \(\mathrm{[}\mathrm{3,}4\mathrm{]}\). The loading sequences are as follows:

The imposed temperature is linear in °C: \(T=1200+300t\)

Reference temperature \({T}_{\mathit{ref}}=1200°C\)