Biomedical Engineering Reference
In-Depth Information
Fig. 3.4 The Kendall peel
test model
appreciably when subjected to the critical force f c needed to debond tendon from
bone, the only material parameter that enters the problem is the fracture energy
G c .
This is the energy per unit area needed to increase the crack length a of the region of
tendon that has debonded from the bone. Using energetic arguments, Rivlin [ 9 ]
calculated the force f c needed to advance the crack:
f c
w ¼
G c
1 cos
' ¼ 90 , this reproduces a simple Griffith-Irwin type fracture criterion. For
approaching 0 , the force needed for extension of a crack between the tendon and
bone approaches infinity. This model is limited, even from the perspective of
elementary linear elastic fracture mechanics. For example, as will be discussed
below, one would expect
. However, even this simple starting
point yields some insight into tendon-to-bone attachment mechanics and might
explain in part why the bone insertions of, for example, the Achilles tendon are such
that there exists a significant overlap region at the heel. The most common site of
tears in the Achilles tendon is not where the tendon first contacts bone but rather
midsubstance, near this point. This is loosely consistent with expectations from this
model: one would not expect a failure at the attachment of tendon to bone with
G c to vary with
close to 0 unless the force f was sufficient to break the tendon itself or to
overwhelm the entire attachment region.
Tendon is compliant compared to bone, so the next appropriate degree of
complexity for a peel test model incorporates an elastic tendon. The solution for
this case was derived by Kendall [ 10 , 11 ] and considers a linear elastic tendon of
elastic modulus E T and thickness t in a state of plane strain, which is appropriate for
w t :
f c
2 E T w 2 t
f c
w þ
G c ¼ð 1 cos
Kendall noted that the elastic term is important only in special cases. The first
case is when
approaches 0 . The second is when the term f c / E T tw is large, which
corresponds to the case of a relatively large strain being reached at the level of f c
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