Today, shape memory alloys (SMAs) have important applications in several fields of science and engineering. This work reports the thermomechanical behavior of NiTi SMA coil springs. The thermomechanical characterization is approached starting from mechanical loading–unloading tests under different electric current intensities, from 0 to 2.5 A. In addition, the material is studied using dynamic mechanical analysis (DMA), which is used to evaluate the complex elastic modulus E* = E^′ − iE^″, obtaining a viscoelastic response under isochronal conditions. This work further evaluates the damping capacity of NiTi SMA using tan δ, showing a maximum around 70 °C. These results are interpreted under the framework of fractional calculus, using the Fractional Zener Model (FZM). The fractional orders, between 0 and 1, reflect the atomic mobility of the NiTi SMA in the martensite (low-temperature) and austenite (high-temperature) phases. The present work compares the results obtained from using the FZM with a proposed phenomenological model, which requires few parameters for the description of the temperature-dependent storage modulus E^′.

Dielectric and thermal properties of polyvinyl butyral (PVB) were studied in this work, using dynamic electrical analysis (DEA) at frequencies from 100 Hz to 1 MHz and temperatures from 293 K to 473 K. Two electrical relaxation processes were investigated: glass transition and interfacial polarization. Above the glass transition temperature (~343 K), interfacial polarization dominates conductive behavior in polyvinyl butyral. The framework of the complex electric modulus was used to obtain information about interfacial polarization. The viscoelastic behavior was analyzed through dynamic mechanical analysis (DMA), where only the mechanical manifestation of the glass transition is observed. The experimental results from dielectric measurements were analyzed with fractional calculus, using a fractional Debye model with one cap-resistor. We were successful in applying the complex electric modulus because we had a good correlation between data and theoretical predictions. The fractional order derivative is an indicator of the energy dissipated in terms of molecular mobility, and the calculated values close to 1 suggest a conductive behavior at temperatures above the glass transition temperature of PVB.

In this work, the viscoelastic behavior of high-density polyethylene (HDPE) and polypropylene (PP) was studied through stress relaxation experiments conducted at different strain levels. The main objective was to evaluate classical, fractional, and conformable derivatives to analyze molecular mobility, using statistical methods to identify the most accurate representation of the viscoelastic response. Besides the coefficient of determination (R²), the average absolute deviation (AAD) and mean squared error (MSE) were used as evaluation metrics, along with a multivariate analysis of variance (MANOVA) and the response surface methodology (RSM) to optimize the correspondence between experimental data and model predictions. The findings demonstrate that the spring-pot, Fractional Maxwell (FMM), Fractional Voigt–Kelvin (FVKM), and Kohlrausch–Williams-Watts (KWW) models effectively describe stress relaxation under statistical criteria. However, a joint analysis using RSM revealed that the choice of mathematical model significantly influences the outcomes. The FVKM was identified as the most effective for HDPE, while the KWW model best characterized PP. These results highlight the importance of optimization tools in advancing the characterization of polymer viscoelasticity. The ability to select the most accurate models for HDPE and PP under varying conditions can directly improve the performance and durability of products in critical industrial sectors such as packaging, automotive, and medical devices, where long-term mechanical behavior is crucial. By offering a framework adaptable to other materials and modeling approaches, this work provides valuable insights for optimizing polymer processing, improving product design, and enhancing the reliability of polymer-based components in a range of industrial applications.