2. Benchmark solution#
2.1. Calculation method used for the reference solution#
Cumulative plastic deformation \(P\) is equal to:
\(P\mathrm{=}\frac{{\sigma }_{L}\mathrm{-}{\sigma }^{y}}{C}\)
with: \({\sigma }_{L}\): constraint to the node in question
\({\sigma }^{y}\): elastic limit
\(C\): slope of the traction curve
The constraints are given by:
\({\sigma }_{\mathit{xx}}({N}_{i})\mathrm{=}\mathrm{-}{P}_{\mathit{res}}({N}_{i})\)
The plastic deformation is given by:
\(\mathrm{\mid }{\varepsilon }_{\mathit{xx}}^{p}({N}_{i})\mathrm{=}P({N}_{i})\mathrm{\mid }\)
2.2. Benchmark results#
Uniaxial stress, plastic deformation, and cumulative plastic deformation are calculated at nodes \({N}_{2}\) and \({N}_{3}\).
For the problem in question:
\({N}_{2}\) |
|
|
\({\sigma }_{\mathit{xx}}\) |
0 |
—300 |
\({\varepsilon }_{\mathit{xx}}\) |
0 |
—6.1658 10—2 |
\({\varepsilon }_{\mathit{xx}}^{p}\) |
0 |
6.1658 10—2 |
2.3. Uncertainty about the solution#
Analytical solution.
2.4. Bibliographical references#
LORENTZ E., PROIX J.M., VAUTIER I., VOLDOIRE F., F., WAECKEL F.: Introduction to thermo-plasticity in the Aster code. Course Reference Manual. EDF - DER, SCE IMA, Dept. Mechanics and Numerical Models, HI-74/96/013/0