PSI - Issue 81

Dmytro Tymoshchuk et al. / Procedia Structural Integrity 81 (2026) 35–40

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in SMAs reflects the phase transitions between martensite and austenite, while the area of the σ – ε loop corresponds to the dissipated energy. The frequency of external loading is one of the key factors that determine the functional properties of SMAs (Iasnii et al., 2024; Tymoshchuk et al., 2024a; Yasniy et al., 2025a). It plays a particularly important role when the material operates under repeated cyclic loading. The loading frequency directly affects the thermal processes inside the material. At high frequencies, self-heating may occur, which can lead to undesirable phase transformations or loss of functionality. It is also an important factor shaping the hysteresis behavior of SMAs. As the frequency increases, the geometry of the hysteresis loop changes, directly affecting its area and, consequently, the level of dissipated energy. Accurate reproduction of the nonlinear hysteresis behavior of SMAs under various loading frequencies is a necessary condition for designing durable components in aerospace, biomedical, and robotic applications. However, classical models often fail to match experimental results, which supports the application of modern machine learning methods to improve prediction accuracy and achieve better agreement with experimental data. Machine learning is applied in various fields of science and engineering. In materials science, it is used to predict the properties of alloys and composites (Yasniy et al., 2024; Yasniy et al., 2025b; Yasniy et al., 2025c). In the financial sector, algorithms are employed to detect fraud and forecast market trends (Tsai et al., 2023; Ahmed et al., 2022). In medicine, artificial intelligence methods assist in diagnosis and treatment prediction (Abbas et al., 2024; Pantanowitz et al., 2025), while in the automotive industry, they are applied to the development of autonomous vehicles (Yang et al., 2021; Navarro et al., 2016). The wide adoption of machine learning across different domains highlights its universality and effectiveness. In the context of SMA research, machine learning opens new opportunities for accurate prediction of material properties. Unlike classical models, machine learning algorithms can account for complex nonlinear relationships among stress, strain, temperature, loading frequency, and other operational factors (Nohira et al., 2025; Guan et al., 2021; Sridharan et al., 2025; Gao et al., 2024; Liu et al., 2025). The aim of this study is to develop an ensemble Voting machine learning model for predicting the hysteresis behavior of SMAs under repeated cyclic loading at different frequencies and to evaluate the accuracy of the obtained predictions.

Nomenclature 

the stress the strain



number of the loading and unloading cycle

N

the frequency

f

2. Material and methods 2.1. Experimental setup and dataset

For this study, the experimental data was obtained from tests performed on a 1.5 mm diameter wire made of Ni 55.8 Ti 44.2 alloy, supplied by Wuxi Xin Xin Glai Steel Trade Co., Ltd. The working length of the wire was 210 mm. In the austenitic state, the material exhibited an elastic modulus of = 52.7 GPa, and the onset of stress-induced phase transformation occurred at = 338 MPa (Iasnii et al., 2022; Iasnii and Junga, 2018). The experiment was conducted at room temperature (approximately 293 K) using an STM-100 servo-hydraulic testing machine. Uniaxial tensile tests were performed under sinusoidal cyclic loading in a stress-controlled mode. During testing, the displacement of the actuator, applied force, and elongation of the wires were recorded. Elongation was measured using a Bi-06 308 extensometer (BISS) with a maximum error of 0.1%, while displacement was measured with a Bi-02-313 inductive sensor, also with an accuracy of ±0.1%. Stress and strain values were determined from the recorded force – elongation relationships obtained using the Test Builder software. The experimental setup ensured the acquisition of high-precision data, which served as the basis for further analysis and modeling of the hysteresis behavior of SMAs under cyclic loading at various frequencies. Based on the test results, a dataset was constructed for training and testing machine learning models. The input features included: • stress σ (МР a) • loading cycle number N • loading/unloading stage indicator (UpDown) The output variable was the strain (%), which characterizes the response of the NiTi alloy to the applied load at different loading frequencies f = (0.3, 0.5, 3, and 5 Hz).