Multiscale FE simulation of diffusion-deformation processes in homogenized dual-porous media

Mathematics and Computers in Simulation

Volumn 82, Issue 10, 2012, Pages 1744-1772

  Rohan, E ^a   Cimrman, R ^a  

^a UNIVERSITY OF WEST BOHEMIA   (Czech Republic)

Author keywords

Double porosity; Fading memory; Fluid saturated porous medium; Homogenization; Multiscale simulation

Indexed keywords

DOUBLE POROSITY; FADING MEMORY; FLUID-SATURATED POROUS MEDIUM; HOMOGENIZATION; MULTI-SCALE SIMULATION;

ASYMPTOTIC ANALYSIS; DIFFUSION IN LIQUIDS; FINITE ELEMENT METHOD; POROSITY; POROUS MATERIALS;

COMPUTER SIMULATION;

EID: 84865707813     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2011.02.011     Document Type: Conference Paper

References (30)

1. T. Arbogast, J. Douglas, and U. Hornung Derivation of the double porosity model of single phase flow via homogenization theory SIAM J. Math. Anal. 21 1990 823 836
2. J.-L. Auriault, and C. Boutin Deformable porous media with double porosity. Quasi statics. I. Coupling effects Transp. Porous Media 7 1 1992 63 82
3. J.-L. Auriault, and C. Boutin Deformable porous media with double porosity. Quasi statics. II. Memory effects Transp. Porous Media 10 2 1993 153 169
4. M.A. Biot General theory of three-dimensional consolidation J. Appl. Phys. 12 1941 155 164
5. R. Cimrman et al., SfePy Simple Finite Elements in Python, 2009. http://sfepy.kme.zcu.cz.
6. D. Cioranescu, A. Damlamian, and G. Griso The periodic unfolding method in homogenization SIAM J. Math. Anal. 40 4 2008 1585 1620
7. D. Cioranescu, and P. Donato An Introduction to Homogenization, Oxford Lecture Series in Mathematics and its Applications 17 1999 Oxford University Press Oxford
8. O. Coussy Poromechanics 2004 John Wiley & Sons
9. S. Cowin Bone Mechanics Handbook 2nd edn. 2001 CRC Press
10. R. de Boer Theory of Porous Media 2000 Springer Berlin
11. H. Ene, and D. Poliševski Model of diffusion in partially fissured media Z. Angew. Math. Phys. 2002 1052 1059
12. A. Frijns, A four-component mixture theory applied to cartilaginous tissues, Ph.D. thesis, Eindhoven University of Technology, 2000.
13. G. Griso, and E. Rohan On the homogenization of a diffusion-deformation problem in strongly heterogeneous media Ricerche Mat. 56 2007 161 188
14. S. Gururaja, H.J. Kim, C.C. Swan, R.A. Brand, and R.S. Lakes Modeling deformation-induced fluid flow in cortical bone's lacunar-canalicular system Ann. Biomed. Eng. 33 2005 7 25
15. U. Hornung Homogenization and Porous Media 1997 Springer Berlin
16. T. Lemaire, S. Naili, and A. Rémond Multi-scale analysis of the coupled effects governing the movement of interstitial fluid in cortical bone Biomech. Model. Mechanobiol. 80 6 2010 1289 1301
17. V. Lukeš, and E. Rohan Microstructure based two-scale modelling of soft tissues Math. Comput. Simul. 65 215 1996 1019 1037
18. A.F. Mak, and J.D. Zhang Numerical simulation of streaming potentials due to deformation-induced hierarchical flows in cortical bone J. Biomech. Eng. 123 1 2001 66 70
19. M. Peszynska Finite element approximation of diffusion equations with convolution terms Math. Comput. 65 215 1996 1019 1037
20. A. Rémond, and S. Naili Transverse isotropic poroelastic osteon model under cyclic loading Mech. Res. Commun. 32 6 2005 645 651
21. E. Rohan Sensitivity strategies in modelling heterogeneous media undergoing finite deformation Math. Comput. Simul. 61 3-6 2003 261 270
22. E. Rohan Modelling large deformation induced microow in soft biological tissues Theor. Comp. Fluid Dyn. 20 2006 251 276
23. E. Rohan, and R. Cimrman Two-scale modelling of tissue perfusion problem using homogenization of dual prous media Int. J. Multiscale Comput. Eng. 8 2010 81 102
24. E. Rohan, R. Cimrman, and V. Lukeš Numerical modelling and homogenized constitutive law of large deforming fluid saturated heterogeneous solids Comput. Struct. 84 2006 1095 1114
25. E. Rohan, and V. Lukeš Homogenization of perfusion in large-deforming medium using the updated lagrangian formulation Proceedings of the ECT 2010 conference, Coburg-Sax Publ 2010
26. E. Rohan, S. Naili, R. Cimrman, T. Lemaire, Multiscale modelling of a fluid saturated medium with double porosity: relevance to the compact bone, submitted for publication.
27. E. Sanchez-Palencia Non-homogeneous Media and Vibration Theory, No. 127 in Lecture Notes in Physics 1980 Springer Berlin
28. R.E. Showalter, D.B. Visarraga, Double-diffusion models from a highly heterogeneous medium, J. Math. Anal. Appl. 295 (2002) 191-210.
29. J. Zeman, and M. Šejnoha From random microstructures to representative volume elements Modell. Simul. Mater. Sci. Eng. 15 2007 325 335
30. D. Zhang, S. Weinbaum, and S. Cowin On the calculation of bone pore water pressure due to mechanical loading Int. J. Solids Struct. 35 1998 4981 4997