Controlling crystallization in soft colloidal systems represents a fundamental challenge for material design. Among different approaches for enhancing the crystal phase, there are evidences that the application of a shear flow may favour the formation of crystals [1,2], thus representing a new method to verify the existence of crystal phases predicted in several soft colloidal systems. In our work we numerically investigate the crystallization of star polymers induced by the presence of a shear flow. Star polymers, i.e. polymer chains anchored to a common centre, represent a favourite model system in soft matter being characterised by a rich phase diagram, encompassing multiple crystal phases. We simulate star-polymers using two Molecular Dynamics approaches: the first is based on SLLOD equations with Gaussian thermostat (MD-GAUSSIAN) and the second uses Dissipative Particle Dynamics thermostat (MD-DPD). The latter has the advantage to implicitly include the hydrodynamic effects of the solvent, which is neglected in the former approach. Our simulations show that a transition from fluid to solid occurs in both types of simulations but the crystals found are of different types, being bcc-like in MD-GAUSSIAN simulations and fcc-like in MD-DPD. Most interestingly, we find that in MD-DPD a two-step crystallization takes place from fluid to bcc and then to fcc, showing the occurrence of a crystal-crystal transition in simulations. This is in agreement with recent experimental results obtained with oscillatory shear flow, thus highlighting the importance of hydrodynamics in the crystallisation process under shear flow. Finally, we discuss what happens during the crystal-crystal transition by comparing our case with the recent work of Peng. Y et al.  on 2D crystallisation of microgel particles.
 G. Petekidis et al., Phys. Rev. E 66, 051402 (2003)
 B. J. Ackerson and P. N. Pusey, Phys. Rev. Lett. 61, 1033 (1998)
 Y. Peng et al., Nature Materials 14, 101-108 (2015)