2. Benchmark solution#
2.1. Calculation method used for the reference solution#
Displacement \(\mathrm{DY}\)
The displacement \(\mathrm{DY}\) referring to point \(C\) corresponds to the imposed displacement.
\(\mathrm{DY}=-0.015(t-1)\)
Constraint \(\mathrm{SIXX}\)
Constraint \(\mathrm{SIXX}\) corresponds to the load applied
Stress \(\mathrm{SIYY}\) and cumulative plastic deformation \(\mathrm{V1}\)
The reference values for stress \(\mathrm{SIYY}\) and cumulative plastic deformation \(\mathrm{V1}\) are non-regression values.
2.2. Reference quantities#
Constraint \(\mathrm{SIXX}\) at point \(C\)
Constraint \(\mathrm{SIYY}\) at point \(C\)
Cumulative plastic deformation \(\mathrm{V1}\) at point \(C\)
Move \(\mathrm{DY}\) to point \(C\)
2.3. Benchmark result#
Grandeur |
Point |
\(\mathrm{Inst}\) |
Reference* |
Reference** |
\(\mathrm{SIXX}(\mathrm{Pa})\) |
\(C\) |
\(2.0\) |
\(-2.0\mathrm{E6}\) |
\(-2.0\mathrm{E6}\) |
\(\mathrm{SIYY}(\mathrm{Pa})\) |
\(C\) |
\(1.07\) |
\(-8.69\mathrm{E6}\) |
\(-8.69\mathrm{E6}\) |
\(1.16\) |
\(-1.39\mathrm{E7}\) |
\(-1.37\mathrm{E7}\) |
||
\(1.34\) |
\(-9.90\mathrm{E6}\) |
\(-9.90\mathrm{E6}\) |
||
\(1.53\) |
\(-9.91\mathrm{E6}\) |
\(-9.90\mathrm{E6}\) |
||
\(\mathrm{V1}\) |
\(C\) |
\(1.07\) |
\(0\) |
\(0\) |
\(1.16\) |
\(1.20E-3\) |
\(1.26E-3\) |
||
\(1.34\) |
\(1.12E-2\) |
\(1.12E-2\) |
||
\(1.53\) |
\(2.01E-2\) |
\(2.01E-2\) |
||
\(\mathrm{DY}(m)\) |
\(C\) |
\(1.07\) |
\(-1.05E-3\) |
\(-1.05E-3\) |
\(1.16\) |
\(-2.40E-3\) |
\(-2.40E-3\) |
||
\(1.34\) |
\(-5.10E-3\) |
\(-5.10E-3\) |
||
\(1.53\) |
\(-7.95E-3\) |
\(-7.95E-3\) |
linear work hardening* parabolic work hardening
2.4. Uncertainty about the solution#
Analytical solution for quantities \(\mathrm{DY}\) and \(\mathrm{SIXX}\)
Digital solution for sizes \(\mathrm{SIYY}\) and \(\mathrm{V1}\)