Constitutive modeling of viscoelastic materials: A quantitative comparison between classic and fractional models

Resumo

Thermoplastic polymers are widely used in biomedical applications, such as knee and hip prosthetics.
The development of optimized orthopedic implants is strongly related to the performance of experimental tests and

computer simulations that approximate the behavior in situ of the material used. The literature indicates the possi-
bility of applying fractional viscoelastic constitutive models as an alternative to the classical integer order models.

However, it is not common to compare quantitatively the results obtained using both approaches. Therefore, the
predictive capabilities of some fractional and classical viscoelastic models with infinitesimal and finite kinematics
are compared in this work. The study is conducted using cyclical and creep-recovery experimental tests at two
strain and stress rates. First we present the individual fittings of the cyclical and creep-recovery experimental data.
Then, these tests are fitted simultaneously. The parameter fitting is made using a hybrid optimization procedure,
using a heuristic method for global search and another based on gradients for local search. In the context of the
experimental conditions evaluated, the results indicated that the use of the fractional models tested did not result in
a significant improvement when the assessment are made using individual experimental data. On the other hand,
for the the simultaneously parameter fitting, the fractional models showed a slight improvement. However, none
of the models used was able to represent satisfactorily the cyclic and creep-recovery data used, this fact may be
related to the presence of nonlinear phenomena not taken into account in the present work.