Industrial components often experience cyclic and dwell loadings variations, making it essential to model their stress-strain response and predict failure to minimize fatigue-related costs. This study presents a modification to the damage evolution rule in the continuum damage viscoplastic model. Based on previous work, the constitutive model integrates unified viscoplasticity, damage evolution, kinematic hardening, and isotropic hardening, with the latter influenced by the radius of the memory surface. The model classifies damage into three components: ductile, fatigue, and creep damage. To improve accuracy, the damage evolution rule was modified by adjusting its components, e.g., making the parameters of fatigue damage component dependent on the effective strain rate to better capture fatigue behaviour at different strain rates. The model was implemented as a standalone code for uniaxial strain- or stress-controlled loadings. Its parameters were identified to match experimental data obtained from AW-2618 aluminum alloy specimens. The dataset includes results from cyclic, creep, and tensile tests, as well as cyclic loading with dwell periods at maximum and minimum strain, all conducted at 195 °C. Parameter identification was conducted using multiple methods, including trial and error, as well as local and global optimization algorithms. The simulated load responses using the identified parameters showed strong agreement with the experimental dataset.