Biomedical Engineering Reference
In-Depth Information
and a certain capacity to support compressive loads in the direction normal to
the fibrous tissue layers. On the other hand, it fails to support traction and shear
forces [50].
The desired condition of structural continuity between the bone and the femoral
shaft arises when an effective adherence, condition known as
bone ingrowth
,
exists between bone cells and the pores of prosthesis covering. This condition
occurs only in the presence of a favorable biomechanical environment that is
frequently related to moderate relative displacements between the surfaces in
contact. Furthermore, other factors influence the bone growth, for instance,
the physiological characteristics of the patient, biocompatibility of the implanted
material, and the characteristics of the porous covering, among others. With the
aim of defining models that are closer to real physics, different studies have
included the modeling of the interface as a new element to be considered [51].
Two main approaches are found in the literature when the interface, in particular,
is considered. The first is the direct incorporation of contact-friction-adherence
conditions between the surfaces. This approach is used, for example, in the works
[16, 32] among others. Another possibility is to assume that the interface is a thin
but volumetric region in which mechanical properties follow a different behavior
from that of the bodies in contact. This approach may be seen in [51].
In this study, the latter approach is followed. The interface is modeled by a thin
volumetric region lying between the bone and the shaft. In this region, volumetric
gasket-type elements are defined. Geometrically, these elements are formed by
two surfaces, upper and lower, and a local coordinate system that distinguishes
(pseudo) normal and tangential directions at each integration point at which the
constitutive problem is described (Figure 2.4). The vector
e
1
corresponds to the
pseudo-normal direction, while
e
2
and
e
3
are perpendicular to this normal direction.
From the kinematic point of view, these elements use the same equations as those
Normal
behavior
Normal
direction
Gasket
Top face (SPOS)
Gasket element node
Membrane
stretch
Midsurface
Bottom face (SNEG)
Membrane
shear
Membrane
stretch
Midsurface
n
4
n
1
8
n
3
n
4
5
7
n
1
n
1
n
2
n
3
n
4
n
2
6
n
3
4
1
n
2
3
2
Figure 2.4
Spatial representation of a gasket element.
