Biomedical Engineering – From Theory to Applications

Orthopaedic Modular Implants Based on Shape Memory Alloys
where:
1 t
wP e e dv
i i
D 457
i i
(24)
e i
i
P
The vectors (ei) depend only on the staple shape. We call Ji the triple integrals which occur
in the relation (24) depend on the temperature, but in a measure much smaller than the
eigenvalues. Therefore the integrals can be considered constants. In this case, by passing to
the limit, the relation becomes:
The temperature variation on time is:
(25)
1
wP Ji
(26)
i i
ctti T T T T e (27)
e e i
Ti = initially temperature of staple; ti = initially value of time; c = a coefficient which depends
on the material thermal conductivity of the staple.
The eigenvalues i of the elasticity matrix depend on the temperature and on the value
ct ti
e . Experimentally, it is demonstrated that the staple deformation is produced with
constant speed. In (Kul’kova et al., 1995) were tested three Nitinol wire specimens: a
commercially available superelastic (W1) wire and two shape memory. It is demonstrated
that the dependence of recovery force function on temperature is linear.
ct ti
Developing in factors series as a function of term e the functions of the proper values
and keeping only the first order term, the variation in time of the compression force exerted
by the staple is done by:
where: Pi is the exerted force at the initial moment ti.
1
ct ti
P Pi f Te; Ti1 e
(28)
c
5.4 Experimental studies for the Nitinol staple
In order to determine the law of variation for the compression force which can be developed
by the Nitinol staple as a function of variable environmental temperature and also to
validate the compression potential of the staple through constant pressure at the
temperature of the human body, we developed an experimental stand (Fig.36).
The experimental stand is made from: -experimental device used to mount the modular
adaptive implant; -Spider 8 – a numerical acquisition system, 12 bits resolution, used to
measure mechanical parameters, such as: forces, mechanical stresses, pressures,
accelerations, velocities, displacements, temperatures.; -S2-100N force transducer, 0.1%
linearity, Hottinger type; -FLIR B200 termographic camera; -IBM ThinkPad R5 notebook.