This paper extends the two time-scale modified phase-field crystal model to examine crystal plasticity. Two non-linear density dependent functions are constructed to effectively represent hydrostatic strain and dislocation density. The functions are then used to develop a new modified phase field crystal model, which accounts for strain and strain-rate couplings on density dynamics. The non-linear additions provide tunable parameters for controlling dislocation climb versus glide, as well as phonon softening mechanisms. A short-wavelength dampening is also introduced to account for phonon scattering and thermoelastic dissipation processes. Finally, a novel semi-implicit numeric scheme for efficient simulations of this model is presented, which also serves as a generalization of the commonly used Fourier pseudo-spectral method. The technique gives rise to unconditionally stable dynamics with simple numeric implementation requirements.