.. _multi_physics-biot_npbc: multi_physics/biot_npbc.py ========================== **Description** Biot problem - deformable porous medium with the no-penetration boundary condition on a boundary region. Find :math:`\ul{u}`, :math:`p` such that: .. math:: \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u}) - \int_{\Omega} p\ \alpha_{ij} e_{ij}(\ul{v}) = 0 \;, \quad \forall \ul{v} \;, \int_{\Omega} q\ \alpha_{ij} e_{ij}(\ul{u}) + \int_{\Omega} K_{ij} \nabla_i q \nabla_j p = 0 \;, \quad \forall q \;, \ul{u} \cdot \ul{n} = 0 \mbox{ on } \Gamma_{walls} \;, where .. math:: D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl} \;. .. image:: /../gallery/images/multi_physics-biot_npbc.png :download:`source code ` .. literalinclude:: /../examples/multi_physics/biot_npbc.py