1. Reference problem#
1.1. Geometry#
It is an 8-node cube, where three faces have zero normal displacement, and the three opposite faces have an imposed and identical normal displacement.
The cube has a side of \(1\mathrm{mm}\). In modeling A, the cube is oriented according to the coordinate system \(\mathrm{Oxyz}\).
Modeling A
1.2. Material properties#
To test the implantation of thermal expansion and desiccation shrinkage, a variable temperature field and a drying field are imposed in such a way that the deformations generated by the two phenomena compensate each other, while considering that the coefficients of thermal expansion and desiccation shrinkage are equal. The values associated with drying have no physical meaning; the test is purely computer based on this point of view.
For the usual linear mechanical characteristics:
Young’s module: |
\(E=32000\mathrm{MPa}\) |
Poisson’s ratio: |
\(\nu =0.18\) |
Coefficient of thermal expansion: |
\(\alpha ={10}^{-5}/°C\) |
Desiccation shrinkage coefficient: |
\(\kappa ={10}^{-5}\) |
Reference temperature |
\({T}_{\mathrm{ref}}=0°C\) |
Reference drying |
\({C}_{\mathrm{ref}}=20\) |
For the non-linear mechanical characteristics of the model **** BETON_DOUBLE_DP **** :
1.3. Boundary conditions and mechanical loads#
Temperature range increasing from \(0°C\) to \(20°C\). |
|
Drying range decreasing from 20 to 0. |
|
Underside of the cube (\(\mathrm{facexy}\)): |
blocked next \(\mathrm{oz}\). |
Top side of the cube (\(\mathrm{face1xy}\)): |
variable displacement imposed in \(\mathrm{mm}\) |
Left side of the cube (\(\mathrm{faceyz}\)): |
blocked next \(\mathrm{ox}\). |
Right side of the cube (\(\mathrm{face1yz}\)): |
variable displacement imposed in \(\mathrm{mm}\) |
Front side of the cube (\(\mathrm{facexz}\)): |
blocked next \(\mathrm{oy}\). |
Back side of the cube (\(\mathrm{face1xz}\)): |
variable displacement imposed in \(\mathrm{mm}\) |
The mechanical load is applied in an imposed displacement on the various faces of the cube. A compression is applied to the face \(\mathrm{face1xz}\), affected by a first multiplying coefficient, and a traction along the faces \(\mathrm{face1xy}\) and \(\mathrm{face1yz}\), affected by a second multiplying coefficient, zero during the first part at the start of loading, is applied, according to the following diagram:
