The role of porosity and solid matrix compressibility on the mechanical behavior of poroelastic tissues

Dehghani, H., Penta, R. and Merodio, J. (2019) The role of porosity and solid matrix compressibility on the mechanical behavior of poroelastic tissues. Materials Research Express, 6(3), 035404. (doi: 10.1088/2053-1591/aaf5b9)

213049.pdf - Accepted Version



We investigate the dependence of the mechanical and hydraulic properties of poroelastic materials on the interstitial volume fraction (porosity) of the fluid flowing through their pores and compressibility of their elastic (matrix) phase. The mechanical behavior of the matrix is assumed of linear elastic type and we conduct a three-dimensional microstructural analysis by means of the asymptotic homogenization technique exploiting the length scale separation between the pores (pore-scale or microscale) and the average tissue size (the macroscale). The coefficients of the model are therefore obtained by suitable averages which involve the solutions of periodic cell problems at the pore-scale. The latter are solved numerically by finite elements in a cubic cell by assuming a cross-shaped interconnected cylindrical structure which results in a cubic symmetric stiffness tensor on the macroscale. Therefore, the macroscale response of the material is fully characterized by six parameters, namely the elastic Young's and shear moduli, Poisson's ratio, the hydraulic conductivity, and the poroelastic parameters, i.e. Biot's modulus and Biot's coefficient. We present our findings in terms of a parametric analysis conducted by varying the porosity as well as the Poisson's ratio of the matrix. Our novel three-dimensional results, which are presented in the context of tumor modeling, serve as a robust first step to (a) quantify the macroscale response of poroelastic materials on the basis of their underlying microstructure, (b) relate the compressibility of the tissue, which can be used to distinguish between benign tumor and cancer, to its microstructural properties (such as porosity), and (c) reveal a nontrivial dependency of Biot's modulus on porosity and compressibility of the matrix, which can pave the way to the optimal design of artificial constructs in terms of fluid volume available for transport of mass and solutes.

Item Type:Articles
Additional Information:HD and JM have been partially supported by the Ministry of Economy in Spain, under the project reference DPI2014-58885-R. HD also acknowledges financial support from the University of Glasgow.
Glasgow Author(s) Enlighten ID:DEHGHANI, HAMIDREZA and Penta, Dr Raimondo
Authors: Dehghani, H., Penta, R., and Merodio, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Materials Research Express
Publisher:IOP Publishing
ISSN (Online):2053-1591
Published Online:19 December 2018
Copyright Holders:Copyright © 2018 IOP Publishing Ltd
First Published:First published in Materials Research Express 6(3):035404
Publisher Policy:Reproduced in accordance with the publisher copyright policy

University Staff: Request a correction | Enlighten Editors: Update this record