Physics-based constitutive model have been successfully applied to the simulation of plastic deformation on the continuum scale. Even though most parameters have a physical meaning and thus a well-defined value range, their large number often makes it hard to find a unique parameter set describing different boundary conditions (strain rate, temperature). It is therefore of great scientific interest to develop ‘parameter-free’ partial models that can be calibrated by lower scale simulations. In this work, annihilation of mobile screw dislocations by cross-slip is formulated in terms of the solute concentration in the aluminium matrix. The cross-slip probability is determined according to the Friedel-Escaig mechanism. The Helmholtz free energy for the partial dislocation constriction is given by molecular dynamics. The stacking fault energy is employed for calculating the stacking fault width of partial screw dislocations as well as the stress-dependent Gibbs free energy. The stacking fault energies for six solute atoms embedded in the matrix were computed using density functional theory simulations following [1]. The stacking fault energy for a multicomponent system is calculated by superposing the binary system results assuming there is no interaction between solute atoms. Finally, the parameter-free cross-slip model is implemented into a dislocation-based hardening model (based on [2]) and well describes the thermally-activated dynamic recovery dominant at the intermediate temperature regime.