Page 51 - Advances in Biomechanics and Tissue Regeneration

3.3 DESIGN METHODOLOGY 45

The relationship between the pressure and change of diameter D and h of the stent may be written as:
πEI ΔD
nr hf θðÞ D
p ¼ 2
and
2EI Δh
r g θðÞ h
p ¼ 2
where f(θ) and g(θ) are geometric functions.
The three mechanisms analyzed, with their respective equations, must be considered as a simplified approach to the
actual mechanical behavior of the stents, which presents complex effects not included in this approach such as plastic
deformations and residual stresses appearing in some conformation processes, frictional resistance in sliding
configurations, etc.

3.3 DESIGN METHODOLOGY

3.3.1 Stent Material
Nitinol is a superelastic alloy capable of reaching very high strain ranges without yielding, allowing complete elastic
recovery. The thermomechanical behavior of this alloy is associated with austenite-martensite phase transformation.
In the martensite phase, the material is easily deformable, and during martensite-austenite transformation under
heating, the material will recover its original shape prior to deformation. Additionally, when the material is deformed
in the austenitic state up to 8%, the stress-induced martensite phenomenon allows the alloy to undergo complete
recoverable deformation. This property is known as superelasticity or rubber-like behavior.
This property makes it possible to design stents that present a soft CEF, allowing a gradual relaxation of the
constriction, and a high RCR, which prevents stent collapse due to external actions (Fig. 3.13).
The alloy used for stent simulation and manufacturing corresponds to an NiTi alloy (50.8 at.% Ni, 49.2 at.% Ti)
supplied by Memory Metalle GmbH (Germany).
Mechanical properties of the material are determined by means of uniaxial tensile tests. In this case, a universal
machine test Instron 5565 has been used, testing standard specimens obtained from sheets 1mm thick. Every test
is done considering complete loading and unloading with displacement control at a reference temperature T 0 ¼22°C.
To simulate material behavior, a phenomenological constitutive model is used, based on the formulation developed
by Auricchio and Taylor [49, 50]. In this respect, the material can be modeled in finite element software (e.g., Abaqus
6.11) as an embedded user material subroutine (UMAT).
Fig. 3.14 shows the average curve of the tensile tested samples versus strain-stress curves resulting from a uniaxial
virtual test simulated and adjusted using the material subroutine implemented in Abaqus 6.11 code for T 0 ¼22°C and
T w ¼37°C, respectively. Thermomechanical parameters, necessary to obtain material behavior at body temperature
T w ¼37°C, are retrieved from the literature [51]. Table 3.2 includes NiTi material mechanical properties fitted to aver-
age values obtained from experimental testing.

FIG. 3.13 Strain-stress curve of
Nitinol alloys. Application of supere-
lastic property to colonic stent
designs. CEF, chronic expansion
force; RCR, radial compression
resistance.

I. BIOMECHANICS