©Freund Publishing House Ltd., International Journal of Nonlinear Sciences & Numerical Simulation 11(10): 817-830, 2010
Effects of Solid Compressibility on Responses of Hydrated Soft
Biological Tissues
Zhaochun Yang
a
'*, Jeen-Shang Lin
b
, Patrick Smolinski
3
a Department ofMechanical Engineering, University of Pittsburgh, Pittsburgh, PA, 15261
b Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh,
PA, 15261
Abstract
The Biot theory and Mixture theory are the two main approaches for the mechanical analysis of
hydrated soft biological tissues. Aside from the fact that the Mixture theory employs an entropy
measure, one main difference between these theories stems from the consideration of the
compressibility of the solid phase. The Biot theory often considers the solid phase to be nearly
incompressible, whereas the Mixture theory considers it to be fully incompressible. The objective of
this study is to investigate the significance of solid compressibility through analytical and numerical
analysis. Both quasi-static and dynamic analyses were carried out on one-dimensional problems for
which the analytical solutions can be derived. The results of the study clearly indicate that the
compressibility of the solid phase can have a significant impact and is an important factor that may
have to be included for soft tissues.
Keywords: Mixture Porous theory; Poroelastic theory; analytic solution; hydrated soft tissue
1. Introduction
Different varieties of soft connective
tissues, such as articular cartilage and
intervertebral disc, exist in the human body.
Significant amounts of mobile fluid, relative to
the solid material, move, impacting the
convection path for transport, heating or
cooling, and the mechanical function of the
structure. Because the electric-chemical
interaction of the mobile fluids with the porous
solid matrix is a complex process, a number of
theoretical models have been developed to
describe this process [1-19].
Theoretically, hydrated soft biological
tissues are considered as a multi-phasic
poroelastic continuum. As Cowin [20] points
* Corresponding Author:
zcyang2010@gmail.com
out, Biot theory and Mixture theory are the
dominant approaches for the mechanical
analysis of biological tissues. Biot theory has
its origin in geomechanics, starting with Biot
work on the consolidation of soils following
Terzaghi's ground breaking work on the
concept of effective stress [21]. Biot theory
builds a model in an average sense by
establishing governing equations over an
infinitesimal volume, whereas the Mixture
theory considers entities surrounding a point.
Mow et al [8] were the first to consider
hydrated soft tissues as a biphasic medium by
using the mixture theory. Their models become
more sophisticated over time with the addition
of the electric-chemical effects [9, 19]. Biot
theory, as exemplified by Simon [2-4], Laible
[5], and Iatridis [6], was later adopted.
The scope of this study encompasses the
biphasic model, the simplest form of the
poroelastic model of tissues. Soft tissues were