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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 71
Numerical Modelling and Homogenized Constitutive Law of Large Deforming Porous Media E. Rohan+ and R. Cimrman*
+Department of Mechanics,
Full Bibliographic Reference for this paper
E. Rohan, R. Cimrman, "Numerical Modelling and Homogenized Constitutive Law of Large Deforming Porous Media", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 71, 2004. doi:10.4203/ccp.79.71
Keywords: large deformation, microstructure, homogenization, porous media, fluid-structure interaction, hereditary creep, numerical modelling, soft tissues.
Summary
In this paper we treat interactions between solid and fluid media at the
microscopic level. This phenomenon is responsible for viscoelastic behaviour
observed at the macroscopic scale where the material model is described in
terms of the homogenized (effective) parameters. Our approach allows to study
relationships between the two scales, pursuing detail interactions of a given
porous material at the scale of the inhomogeneities. The so-called micromodel is based on that of Biot,
cf. [1]; here we consider its
quasi-static version extended for large deformation by considering the
stress-equilibrium equation in terms of the incremental updated Lagrangian (UL)
formulation. The micromodel is defined for finite inhomogeneities of the scale
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The homogenization for
By virtue of the homogenization method, cf. [2],
one obtains the following effective
material coefficients: the homogenized tangent stiffness tensor
As a particular microstructure we consider material with quasi-periodic
distribution of fluid capsules embedded in the porous matrix. In this situation
the macroscopic pressure The multiscale approach seems to be promising for application in biomechanics, where the coupling between dissipative processes related to the induced viscoelasticity and microflow is essential, and is responsible for redistribution of dissolved species with relationships to growth and tissue remodelling. In Figure IRefrohan:fig the deformation and perfusion through microstructure of smooth muscle cell is illustrated for two time instants of the contraction process. We discuss numerical aspects of the modelling. (The research has been supported generously by the project LN00B084 of The New Technologies Research Centre in Pilsen.) References
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