.. _multi_physics-thermo_elasticity_ess: multi_physics/thermo_elasticity_ess.py ====================================== **Description** Thermo-elasticity with a computed temperature demonstrating equation sequence solver. Uses dw_biot term with an isotropic coefficient for thermo-elastic coupling. The equation sequence solver ('ess' in solvers) automatically solves first the temperature distribution and then the elasticity problem with the already computed temperature. Find :math:\ul{u}, :math:T such that: .. math:: \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u}) - \int_{\Omega} (T - T_0)\ \alpha_{ij} e_{ij}(\ul{v}) = 0 \;, \quad \forall \ul{v} \;, \int_{\Omega} \nabla s \cdot \nabla T = 0 \;, \quad \forall s \;. where .. math:: D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl} \;, \\ \alpha_{ij} = (3 \lambda + 2 \mu) \alpha \delta_{ij} \;, :math:T_0 is the background temperature and :math:\alpha is the thermal expansion coefficient. Notes ----- The gallery image was produced by (plus proper view settings):: ./postproc.py block.vtk -d'u,plot_displacements,rel_scaling=1000,color_kind="scalars",color_name="T"' --wireframe --only-names=u -b .. image:: /../doc/images/gallery/multi_physics-thermo_elasticity_ess.png :download:source code  .. literalinclude:: /../examples/multi_physics/thermo_elasticity_ess.py