Advanced

A Superposition Procedure for Calculation of Effective Diffusion and Elastic Parameters of Sparsely Porous Materials

ALI, ABDALLAH SHOKRY MAHMOUD LU ; Lindberg, Gustav LU ; Kharmanda, Mohamed Ghias LU and Ståhle, Per LU (2017) In Transport in Porous Media
Abstract
Effective material parameters for diffusion and elastic deformation are calculated
for porous materials using a continuum theory-based superposition procedure. The theory that is limited to two-dimensional cases, requires that the pores are sufficiently sparse. The method
leads to simple manual calculations that can be performed by, e.g. hospital staff at clinical
diagnoses of bone deceases that involve increasing levels of porosity. An advantage is that the
result relates to the bone material permeability and stiffness instead of merely pore densities.
The procedure uses precalculated pore shape factors and exact size scaling. The remaining
calculations do not require any knowledge of the underlying field methods... (More)
Effective material parameters for diffusion and elastic deformation are calculated
for porous materials using a continuum theory-based superposition procedure. The theory that is limited to two-dimensional cases, requires that the pores are sufficiently sparse. The method
leads to simple manual calculations that can be performed by, e.g. hospital staff at clinical
diagnoses of bone deceases that involve increasing levels of porosity. An advantage is that the
result relates to the bone material permeability and stiffness instead of merely pore densities.
The procedure uses precalculated pore shape factors and exact size scaling. The remaining
calculations do not require any knowledge of the underlying field methods that are used to
compute the shape factors. The paper establishes the upper limit for the pore densities that are
sufficiently sparse. A cross section of bovine bone is taken as an example. The superposition
procedure is evaluated against a full scale finite element calculation. The study compares the
pore induced change of the diffusion coefficient and elastic modulus. The predictions differ
between superposition and full scale calculations with 0.3% points when pore contribution
to the diffusion constant is 3–7%, and 0.7% points when the pore contribution to the modulus
of elasticity is 4.5–5%. It is uncertain if the error is in the superposition method, which is
exact for small pore densities, while the full scale finite model is not. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
in
Transport in Porous Media
pages
22 pages
publisher
Kluwer
external identifiers
  • scopus:85019103149
  • wos:000403696900008
ISSN
0169-3913
DOI
10.1007/s11242-017-0866-4
language
English
LU publication?
yes
id
87b04abf-3e5e-4ce1-ad95-fe61cb025e9c
date added to LUP
2017-05-16 22:27:19
date last changed
2018-01-07 12:03:54
@article{87b04abf-3e5e-4ce1-ad95-fe61cb025e9c,
  abstract     = {Effective material parameters for diffusion and elastic deformation are calculated<br/>for porous materials using a continuum theory-based superposition procedure. The theory that is limited to two-dimensional cases, requires that the pores are sufficiently sparse. The method<br/>leads to simple manual calculations that can be performed by, e.g. hospital staff at clinical<br/>diagnoses of bone deceases that involve increasing levels of porosity. An advantage is that the<br/>result relates to the bone material permeability and stiffness instead of merely pore densities.<br/>The procedure uses precalculated pore shape factors and exact size scaling. The remaining<br/>calculations do not require any knowledge of the underlying field methods that are used to<br/>compute the shape factors. The paper establishes the upper limit for the pore densities that are<br/>sufficiently sparse. A cross section of bovine bone is taken as an example. The superposition<br/>procedure is evaluated against a full scale finite element calculation. The study compares the<br/>pore induced change of the diffusion coefficient and elastic modulus. The predictions differ<br/>between superposition and full scale calculations with 0.3% points when pore contribution<br/>to the diffusion constant is 3–7%, and 0.7% points when the pore contribution to the modulus<br/>of elasticity is 4.5–5%. It is uncertain if the error is in the superposition method, which is<br/>exact for small pore densities, while the full scale finite model is not.},
  author       = {ALI, ABDALLAH SHOKRY MAHMOUD and Lindberg, Gustav and Kharmanda, Mohamed Ghias and Ståhle, Per},
  issn         = {0169-3913},
  language     = {eng},
  month        = {05},
  pages        = {22},
  publisher    = {Kluwer},
  series       = {Transport in Porous Media},
  title        = {A Superposition Procedure for Calculation of Effective Diffusion and Elastic Parameters of Sparsely Porous Materials},
  url          = {http://dx.doi.org/10.1007/s11242-017-0866-4},
  year         = {2017},
}