Thermoelastic Stress

Problem description

We solve a thermo-mechanical homogeneous model in cube domain. The dimensions of this cube model are 1 m in all directions. The boundary conditions and temperature loadings, as well as the material can refer Chapter 14 in Kolditz et al. \cite Kolditz2012 for detailed problem description.

Results and evaluation

Result showing temperature and stresses development with time in the centre node of the model:

The analytical solution of stresses after heating is: \[\begin{equation} \sigma_{xx} = \sigma_{yy} = \sigma_{zz} = - \frac{\alpha \Delta T E}{1 - 2 \nu} = - 3.260869\, \textrm{MPa} \end{equation}\]

The relative error between the numerical simulation and the analytical solution is 9.2⋅10^-13.

References

Kolditz, O. and Görke, U.-J. and Shao, H. and Wang, W. (2012): Thermo-Hydro-Mechanical-Chemical Processes in Porous Media - Benchmarks and Examples. vol. 86, ISBN: 978-3-642-27176-2, Springer, DOI: 10.1007/978-3-642-27177-9