Functionally Graded Materials in Engineering - Structural Interfaces and Attachments in Biology - page 32

Functional grading at the tendon-to-bone insertion site involves several
mechanisms, including variations of the collagen fiber orientation from tendon to
bone and a gradual variation of the mineral content. While the fibers that are
uniaxially oriented in the tendon exhibit angular variations as they approach the
bone, the mineral content varies from high volume fraction at the bone surface to
zero at the tendon-insertion boundary. This phenomenon and its implications on the
stiffness of the insertion site and the local stress concentration have recently been
investigated [ 11 , 91 , 92 ].
Studies of a potential for FGM in hip replacement stems have also been
conducted. For example, potential advantages of a 2-D functionally graded stem
with variable content of hydroxyapatite, bioglass, and collagen were considered
[ 93 ]. As was illustrated in this study, stress shielding and interfacial shear stress at
the stem-femur interface were dramatically reduced compared to a standard tita-
nium stem.
Dental applications of FGM have also received close attention. In particular,
Hedia [ 94 ] conducted design of a dental implant coating and illustrated that if it
is graded from titanium at the apex to collagen at the root, the von Mises stress in
the bone can be reduced by 17% compared to the stress with hydroxyapatite
coating. Further studies of the effect of graded implants on the bone can be found
in [ 95 ].

2.5 Example Problem: Optimization of an FGM Sandwich
Panel for Maximum Buckling Load and Fundamental
Frequency

Contrary to numerous FGM studies where grading was limited to the thickness
direction, it is interesting to quantify potential advantages of in-surface grading in
engineering and biomimetic structures. Such analysis is of particular interest since
in-surface grading is found in numerous biological systems, such as the previously
discussed tendon-to-bone insertion site.
In the present section, we consider the effect of optimized grading of the in-plane
stiffness in sandwich plates aiming at an increase in the eigenvalues (buckling load
and fundamental frequency), without a penalty in the plate weight. The size of the
sandwich plate considered in the study was 1 01 m. Each facing was

constructed of 11 cross-ply 0.125 mm thick IM7/977-2 carbon/epoxy layers with
the lamination scheme [0 3 /90/0 3 /90/0 3 ]. The fiber volume fraction in all layers of
the original plate (prior to the introduction of grading) was 50%. The 7.25 mm thick
foam core was manufactured from Divinycell HT 65.
The boundaries of the plate were simply supported. In the buckling problem, in-
plane displacements of the edges loaded by compressive stress resultants were
unconstrained in the load direction, while their tangential in-plane displacements
(displacements along the edge) were prevented. Such boundary conditions

: 0 1 : 0 0 :