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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 89
Edited by: M. Papadrakakis and B.H.V. Topping
Paper 41

Computational Homogenization of Perfused Deforming Tissues

E. Rohan, R. Cimrman and V. Lukeš

Department of Mechanics, Faculty of Applied Sciences, University of West Bohemia, Plzen, Czech Republic

Full Bibliographic Reference for this paper
, "Computational Homogenization of Perfused Deforming Tissues", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 41, 2008. doi:10.4203/ccp.89.41
Keywords: fluid saturated porous materials, multiscale modeling, homogenization, tissue perfusion, fading memory, finite element method.

The aim of this paper is to present the periodic homogenization-based methodology of the two-scale computational modeling of fluid saturated porous media. We summarize the computational multiscale modeling of fluid saturated porous media with potential applications in tissue biomechanics. The methodology is based upon the homogenization of locally periodic double porous materials with various topological arrangements of primary and dual porosities.

The main features of this approach are the Biot model with scale dependent permeability and the microstructure topology. In both cases reported here the dual porous matrix is connected, the difference is related to connectivity of highly permeable sectors: in the first case there are two mutually separated such sectors, the limit model is featured by separated (parallel) flows with fading memory effects, in the second case we consider disconnected inclusions, so that the limit model degenerates into a viscoelastic solid.

Using theoretical results of the homogenization procedure [1,2,3], here we present the upscaled models in the finite element discretized form and describe the computational procedure which recently was implemented in the SfePy in-house developed software [4].

E. Rohan, "Modelling large deformation induced microflow in soft biological tissues", Theor. Comput. Fluid Dynamics, 20, 251-276, 2006. doi:10.1007/s00162-006-0020-3
E. Rohan, R. Cimrman, V. Lukeš, "Numerical modelling and homogenized constitutive law of large deforming fluid saturated heterogeneous solids", Computers and Structures, 84, 1095-1114, 2006. doi:10.1016/j.compstruc.2006.01.008
G. Griso and E. Rohan, "On homogenization of diffusion-deformation problem in strongly heterogeneous media", Ricerche di Matematica, 56, 161-188, 2007. doi:10.1007/s11587-007-0011-8
R. Cimrman, et al., SfePy home page,, 2008.

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