Comparative Study of the Viscoelastic Behavior on PLA Filaments, a Fractional Calculus Approach

The focus of this work is to present a comparative study of the classical and fractional rheological models for predicting the viscoelastic behavior of polylactic acid (PLA) filaments. Stress relaxation tests were carried out at isothermal conditions, and to obtain a better description of experimental results, we used the spring-pot element, which represents an intermediate behavior between a spring (elastic response) and a dashpot (viscous response). Furthermore, the fractional differential equation was established according to the Caputo’s derivative definition. Therewith, the models used are Maxwell and Voigt-Kelvin, the solution of rheological models with Caputo fractional derivative resulting in a Mittag-Leffler function, while the use of conformable derivative results in a KWW function. The experimental data obtained by stress relaxation tests show a fractional order of values between 0 and 1, which are related to the molecular mobility of the material under study.