The secondary air system and cooling passages of gas turbine components are prone to blockage from sand and dust. Prediction of deposition requires accurate models of particle transport and thermo-mechanical interaction with walls. Bounce stick models predict whether a particle will bounce, stick, or shatter upon impact and calculate rebound trajectories if applicable. This paper proposes an explicit bounce stick model that uses analytical solutions of adhesion, plastic deformation and viscoelasticity to time-resolve collision physics. The Discrete-Element Methods (DEM) model shows good agreement when compared to experimental studies of micron and millimetre-scale particle collisions, requiring minimal parametric fitting. Non-physical values mechanical properties, artifices of previous models, are thus eliminated. Further comparison is made to the best resolved and industry standard semi-empirical models available in literature. In addition to coefficients of restitution, other variables crucial to accurately model rebound, for example angular velocity, are predicted. The time-stepping explicit approach allows full coupling between internal processes during contact, and shows that particle deformation and hence viscoelasticity play a significant role in adhesion. Modelling time-dependent internal variables such as wall-normal force create functionality for future modelling of arbitrarily shaped particles, the physics of which has been shown by previous work to differ significantly from that of spheres. To date these effects have not been captured well using by higher-level energy-based models.