Shape memory alloys (SMAs), particularly NiTi-based alloys, exhibit functional fatigue under cyclic thermomechanical loading, characterized by permanent strain accumulation, recovery strain reduction, and hysteresis shifts, which degrade long-term performance. This study presents a simplified and accurate model based on a modified Boltzmann sigmoidal (MBS) function, where the original parameters were systematically redefined to represent key SMA properties, such as recovery strain, permanent strain, transformation temperature, and cycle number. The model was developed and validated using experimental data obtained from NiTi SMA samples subjected to 500 cycles at constant stress levels (50 MPa and 60 MPa), with strain measurements captured using a high-resolution LASER displacement sensor. The MBS model effectively predicted the exponential evolution of recovery and permanent strains with increasing cycles and achieved a high curve-fitting accuracy (R² > 0.98). Compared to complex models like the Limiting Loop Proximity (L2P) model, the proposed approach is computationally efficient, easy to implement, and requires minimal calibration, making it well-suited for practical engineering applications involving SMA-based components operating under cyclic conditions.