4D Numerical Analysis of Scaffolds: A New Approach - Tissue Engineering: Computer Modeling, Biofabrication and Cell Behavior - page 69

tissue engineering scaffolds [ 24 ], biodegradable ligaments [ 51 ], biodegradable en-
dovascular [ 8 ] and urethral stents [ 42 ]. The design process must contemplate the
biocompatibility issues related to toxicity and the functional aspect related to me-
chanical considerations. In terms of mechanical dimensioning, one must consider
not only the static strength and stiffness of the device, but also the long-term me-
chanical behavior considering degradation. This degradation is defined as the time-
dependent cumulative irreversible damage due to hydrolysis.
When loading conditions are simple and the desired time for mechanical support
is known, a “trial and error” approach may be enough to design reasonable reliable
scaffolds. In more complex situations, engineers and designers can use numerical
approaches to define the material formulation and geometry that will satisfy the im-
mediate needs of symptomatic relief, without the occurrence of any degradation,
using conventional dimensioning. However, the lack of design tools to predict long
term behavior has limited the success of biodegradable scaffolds. The considera-
tions and the dimensioning methods developed until this moment may overcome
this limitation, normally, providing a poor solution. Therefore, it is necessary to
propose new approaches to improve the solution for this problem.
In this chapter, a new numerical approach, which can use hyper elastic constitu-
tive models, such as the Neo-Hookean, the Mooney-Rivlin and the second reduced
order will be discussed. In fact, the new approach consists on a constitutive model
and a failure criterion, which are implemented in commercial finite element soft-
ware packages like ABAQUS via User Material (UMAT) subroutine and Python
language. Through a failure criterion, the degradation rate was used to define the
strength of the material at a given degradation time, using a first order kinetic equa-
tion. The material parameters of the constitutive model were calculated by inverse
parameterization of the model compared against experimental data. It was found
that only one material parameter varies linearly with the hydrolytic damage (which
depends on the degradation time). Although this approach was evaluated based on
experimental tensile tests of fibers, for a particular blend of polylactic acid (PLA)
and polycaprolactone (PCL), the authors believe that this can be extended to other
thermoplastic biodegradable materials with response similar to hyper elastic behav-
ior. The new numerical approach was able to predict the load-displacement plot with
reasonable accuracy until 50 % of hydrolytic damage. It can be further extended to
numerical 3D models and complex loading scenarios for different applications, to
predict the long-term mechanical behavior.
2 Biodegradable Polymers
Biodegradable polymers can be classified as either naturally derived polymers or
synthetic polymers. A large range of mechanical properties and degradation rates
are possible among these polymers. However, each of these may have some short-
comings, which restrict its use for a specific application, due to inappropriate stiff-
ness or degradation rate. Blending, copolymerization or composite techniques are