.. _linear_elasticity-prestress_fibres: linear_elasticity/prestress_fibres.py ===================================== **Description** Linear elasticity with a given prestress in one subdomain and a (pre)strain fibre reinforcement in the other. Find :math:\ul{u} such that: .. math:: \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u}) + \int_{\Omega_1} \sigma_{ij} e_{ij}(\ul{v}) + \int_{\Omega_2} D^f_{ijkl} e_{ij}(\ul{v}) \left(d_k d_l\right) = 0 \;, \quad \forall \ul{v} \;, where .. math:: D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl} \;. The stiffness of fibres :math:D^f_{ijkl} is defined analogously, :math:\ul{d} is the unit fibre direction vector and :math:\sigma_{ij} is the prestress. Visualization ------------- Use the following to see the deformed structure with 10x magnified displacements:: \$ ./postproc.py block.vtk -b --vector-mode=warp_norm -s 1 --wireframe .. image:: /../gallery/images/linear_elasticity-prestress_fibres.png :download:source code  .. literalinclude:: /../examples/linear_elasticity/prestress_fibres.py