.. _homogenization-linear_homogenization_up: homogenization/linear_homogenization_up.py ========================================== **Description** Compute homogenized elastic coefficients for a given heterogeneous linear elastic microstructure, see [1] for details or [2] and [3] for a quick explanation. The mixed formulation, where displacements and pressures are as unknowns, is used in this example. [1] D. Cioranescu, J.S.J. Paulin: Homogenization in open sets with holes. Journal of Mathematical Analysis and Applications 71(2), 1979, pages 590-607. https://doi.org/10.1016/0022-247X(79)90211-7 [2] J. Pinho-da-Cruz, J.A. Oliveira, F. Teixeira-Dias: Asymptotic homogenisation in linear elasticity. Part I: Mathematical formulation and finite element modelling. Computational Materials Science 45(4), 2009, pages 1073-1080. http://dx.doi.org/10.1016/j.commatsci.2009.02.025 [3] J. Pinho-da-Cruz, J.A. Oliveira, F. Teixeira-Dias: Asymptotic homogenisation in linear elasticity. Part II: Finite element procedures and multiscale applications. Computational Materials Science 45(4), 2009, pages 1081-1096. http://dx.doi.org/10.1016/j.commatsci.2009.01.027 :download:`source code ` .. literalinclude:: /../sfepy/examples/homogenization/linear_homogenization_up.py