Numerical Modeling of the Stress-Strain Behavior of Synthetic Multifilaments Under Progressive Dynamic Loading Cycles

Abstract

This study presents a numerical approach for simulating the stress-strain behavior of high-modulus polyethylene (HMPE) and polyester (polyethylene terephthalate, PET) multifilaments subjected to progressive dynamic tensile loading cycles. Experimental tests were performed under force-controlled conditions, with a fixed frequency of 0.1 Hz and sinusoidal waveform, considering five successive zero-tension loading cycles with increasing amplitudes from 0 to 50% of the Yarn Break Load (YBL). The numerical modeling was carried out using a phenomenological hyperelastic Modified Yeoh model, implemented within a tensor-based formulation grounded in continuum mechanics and calibrated through parametric optimization based on experimental data. The simulations demonstrated a satisfactory ability to reproduce the constitutive response of both fibers across different load levels, even under non-stabilized hysteresis conditions. The results showed that the mean simulation error varied between cycles, with the largest discrepancies observed for the first cycle at the lowest load amplitude (0 to 10% of the YBL). Conversely, the highest load amplitude cycle (0 to 50% of the YBL) exhibited the best visual agreement between numerical and experimental curves for both HMPE and PET. Overall, a general trend of decreasing mean error was observed with increasing load amplitude and number of cycles. The identified phenomenological parameters remained consistent throughout the simulations, indicating the robustness of the implemented numerical code, although these parameters do not possess direct physical or mechanical meaning. The results highlight the exploratory nature of the study and support the potential of the proposed methodology for future extensions, including other synthetic fibers, higher structural levels, and investigations involving different loading frequencies, rates, and non-stabilized single-cycle loading conditions.