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Page 12 of 15 Qiu et al. Vessel Plus 2018;2:12 I http://dx.doi.org/10.20517/2574-1209.2018.13

Stress (MPa)

Strain
Figure 10. Experimental and simulated stress-strain behaviours of blended PLA/PBS (70/30) for different strain rates [50]

with degradation . At human-body temperature, the biodegradation process is a combined effect of time
[48]
and local deformation. To study this process appropriately, it is necessary to couple the visco-deformation
model with biodegradation. In this case, a damage tensor needs to be introduced into the model to simulate
the material degradation process, linked with the multi-axial stress/strain states in the implanted stent.
The evolution of this damage tensor will depend on mechanical deformation and subsequently affect the
mechanical properties as a result of material degradation . In this way, the interplay between deformation
[49]
and degradation can be modelled, including the influence of deformation rate and material composition,
which has not been previously reported for biodegradable polymeric stents . This type of model, although
[44]
not available yet, can best simulate the degradation process and help predict the biological outcome due to
progressively changing load-bearing property of vascular implant during degradation process.

Loading rate dependency
It is well known that PLLA has low mechanical strength and poor elongation compared to metal, which
limits its application for stents. Based on literature review, a number of experimental studies have been
performed to investigate and improve the mechanical behaviour of PLA, including adding plasticizers to
PLA and blending PLA with ductile biodegradable polymers. Also, different constitutive material models
(e.g., elastic-plastic model and viscoelastic model) were applied to model the deformation of PLLA stent. It
should be noted that the stress-strain behaviour of polymers is affected by strain rate, which indicates the
time-dependent deformation nature of the materials (an increase of stress level with the increase of loading
rate). Consequently, consideration of the time-dependent or viscous behaviour of the materials should be
given during the process of designing and manufacturing of polymeric devices, including computational
studies.

Only recently, Qiu et al. applied an elastic-plastic constitutive model with time dependency to model free
[50]
expansion of Elixir stent under a loading rate of 1.4, 14 and 140 MPa/s, respectively. Loading-rate dependence
was described by inputting the ratio of yield stress as a function of plastic-strain rate. As shown in Figure 10, the
rate-dependent stress-strain response of a PLA and poly-butylene-succinate (PBS) copolymer (with a weight
ratio of 70% to 30%) was simulated very well by the rate-dependent elastic-plastic model . After expansion,
[50]
stresses developed in the stent was dependent on the loading rates, for both magnitude and distribution.
Stent recoiling showed a significant reduction when the loading rate was changed from 1.4 to 140 MPa/s, as