@Article{IJNAM-1-1,
author = {Zhangxin, Chen and Stephen, Lyons, L. and Qin, Guan},
title = {The Mechanical Behavior of a Poroelastic Medium Saturated with a Newtonian Fluid},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2004},
volume = {1},
number = {1},
pages = {75--98},
abstract = {<p style="text-align: justify;">In this paper we systematically derive, via the theory of homogenization, 
the macroscopic equations for the mechanical behavior of a deformable
porous medium saturated with a Newtonian fluid. The derivation is first based
on the equations of linear elasticity in the solid, the Stokes equations for the
fluid, and suitable conditions at the fluid-solid interface. A detailed comparison
between the equations derived here and those by Biot is given. The 
homogenization approach determines the form of the macroscopic constitutive 
relationships between variables and shows how to compute the coefficients in these
relationships. The derivation is then extended to the nonlinear Navier-Stokes
equations for the fluid in the deformable porous medium for the first time. A
generalized Forchheimer law is obtained to take into account the nonlinear 
inertial effects on the flow of the Newtonian fluid through such a medium. Both
quasi-static and transient flows are considered in this paper. The properties
of the macroscopic coefficients are studied. The computational results show
that the macroscopic equations predict well the behavior of the microscopic
equations in certain reasonable test cases.</p>},
issn = {2617-8710},
doi = {https://doi.org/2004-IJNAM-967},
url = {https://global-sci.com/article/83893/the-mechanical-behavior-of-a-poroelastic-medium-saturated-with-a-newtonian-fluid}
}