This plane strain condition validation case belongs to solid mechanics. The aim of this test case is to validate the following parameters:
The simulation results from SimScale were compared to the analytical results presented in [SSLV04]\(^1\).
The geometry used for the case is as follows:
The 3D geometry is a 45\(^0\) section of a hollow cylinder with dimensions as tabulated below:
| A | B | E | F | A’ | B’ | E’ | F’ | |
| x | 0.1 | 0.2 | 0.0707 | 0.1414 | 0.1 | 0.2 | 0.0707 | 0.1414 |
| y | 0 | 0 | 0.0707 | 0.1414 | 0 | 0 | 0.0707 | 0.1414 |
| z | 0 | 0 | 0 | 0 | 0.01 | 0.01 | 0.01 | 0.01 |
Tool Type: Code Aster
Analysis Type: Static linear
Mesh and Element Types: The meshes used in case (A) and (B) were created using the standard mesher on the SimScale platform, while the meshes used in case (C) and (D) were created in an external platform and then imported to the SimScale workbench.
| Case | Mesh Type | Number of Nodes | Element Type |
| (A) | linear tetrahedral | 32553 | Standard |
| (B) | quadratic tetrahedral | 239421 | Standard |
| (C) | linear hexahedral | 768 | Standard |
| (D) | quadratic hexahedral | 2720 | Standard |
Material:
Boundary Conditions:
The analytical solution is given by the equations presented under Reference Solution\(^1\).
The results obtained from SimScale for displacements, stresses, and strains at point A are compared with those presented in [SSLV04].
| Case | Quantity | [SSLV04] | SimScale | Error (%) |
| (A) | Displacement \(dx\ [m]\) | 5.90e-05 | 5.72e-05 | -3.05 |
| (B) | Displacement \(dx\ [m]\) | 5.90e-05 | 5.72e-05 | -3.05 |
| (C) | Displacement \(dx\ [m]\) | 5.90e-05 | 5.71e-05 | -3.22 |
| (D) | Displacement \(dx\ [m]\) | 5.90e-05 | 5.71e-05 | -3.22 |
| (A) | Cauchy Stress \(\sigma_{xx}\ [MPa]\) | -6.00e01 | -5.89e01 | -1.83 |
| (B) | Cauchy Stress \(\sigma_{xx}\ [MPa]\) | -6.00e01 | -5.99e01 | -0.16 |
| (C) | Cauchy Stress \(\sigma_{xx}\ [MPa]\) | -6.00e01 | -5.12e01 | -14.67 |
| (D) | Cauchy Stress \(\sigma_{xx}\ [MPa]\) | -6.00e01 | -5.98e01 | -0.33 |
| (A) | Cauchy Stress \(\sigma_{yy}\ [MPa]\) | 1.00e02 | 1.00e02 | 0 |
| (B) | Cauchy Stress \(\sigma_{yy}\ [MPa]\) | 1.00e02 | 1.00e02 | 0 |
| (C) | Cauchy Stress \(\sigma_{yy}\ [MPa]\) | 1.00e02 | 1.03e02 | 3 |
| (D) | Cauchy Stress \(\sigma_{yy}\ [MPa]\) | 1.00e02 | 0.99e02 | -1 |
| (A) | Total Strain \(\epsilon_{xx} \) | -4.50e-04 | -4.63e-04 | 2.89 |
| (B) | Total Strain \(\epsilon_{xx} \) | -4.50e-04 | -4.67e-04 | 3.78 |
| (C) | Total Strain \(\epsilon_{xx} \) | -4.50e-04 | -4.34e-04 | -3.55 |
| (D) | Total Strain \(\epsilon_{xx} \) | -4.50e-04 | -4.67e-04 | 3.78 |
| (A) | Total Strain \(\epsilon_{yy} \) | 5.90e-04 | 5.72e-04 | -3.05 |
| (B) | Total Strain \(\epsilon_{yy} \) | 5.90e-04 | 5.72e-04 | -3.05 |
| (C) | Total Strain \(\epsilon_{yy} \) | 5.90e-04 | 5.71e-04 | -3.22 |
| (D) | Total Strain \(\epsilon_{yy} \) | 5.90e-04 | 5.71e-04 | -3.22 |
Find figure 4 below for the total strain \(\epsilon_{yy}\) distributed across the cylinder:
Last updated: July 20th, 2020
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