Biomedical Engineering Reference
In-Depth Information
the time and spatially varying fluid pressure field (or fluid velocity), thus making
analytical solutions more difficult to compute than for standard viscoelastic con-
stitutive models. Because of this, quasianalytic solutions to biphasic problems have
only been obtained for simplified geometries and loading scenarios [
119
,
205
]. These
include the confined and unconfined loading of a cylinder subjected to ramp loading,
step loading, and harmonic loading [
119
,
205
] for linear material behavior, and for
certain nonlinear materials [
206
,
207
]. Both flow-dependent (e.g., biphasic mater-
ial) and flow-independent mechanisms may be needed to accurately describe and
predict the apparent viscoelasticity of some biological soft tissues [
207
,
208
]. Poro-
viscoelastic formulations have been proposed that utilize a viscoelastic continuum
model within the solid phase. These approaches have found utility in the field of
cartilage mechanics [
207
-
209
].
8.3.4 Computational Modeling
Analytical solutions to the equations of motion for the mechanics of ligaments and
tendons can only be obtained for simplified geometries and loading scenarios (e.g.,
uniaxial tension-compression). For complex geometries and loading patterns such
as simulation of the mechanics of a ligament within an intact joint, the geometry and
governing equations must be discretized and solved numerically [
34
,
120
]. The FE
method is by far the most commonly used numerical method in the field of biosolid
mechanics. Commercial and freely available software packages support preprocess-
ing, solution, and postprocessing ofthe nonlinear FE problems. Many studies in the
literature have used FE methods for the simulation of ligament and tendon mechan-
ics (e.g., [
29
,
32
,
44
,
120
]). In addition to elastic problems, the FE method can also
be used to solve viscoelastic problems and biphasic problems. In the past, address-
ing these types of problems was more difficult due to the lack of a FE framework
specifically designed for biological applications. To address this issue, our lab devel-
oped FEBio, a nonlinear implicit finite element framework designed specifically for
analysis in computational solid biomechanics
(
www.febio.org
)
[
210
].
8.3.5 Homogenization
Although continuum-based constitutive models are useful for describing macro-
scopic behavior, they do not address the mechanical behavior that occurs at lower
length scales and are not always useful for the study of structure-function relation-
ships between the microscale and the macroscale. Because of the multiscale structure
of ligaments and tendons, it is sometimes desirable to use models that can simultane-
ously describe both macroscale and microscale behavior. This is the goal of multiscale
modeling in mechanics, and homogenization is part of the foundation of multiscale
modeling. Homogenization is the process of obtaining a macroscopic stress-strain
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