A three-dimensional large-sliding contact model coupled with strain-induced phase transformations (PTs) and plastic flow in a disk-like sample under torsion at high pressure in rotational diamond anvil cell (RDAC) is formulated and studied. Coulomb and plastic friction are combined and take into account variable parameters due to PT. Results are obtained for weaker, equal-strength, and stronger high pressure phases, and for three values of the kinetic coefficient in a strain-controlled kinetic equation and friction coefficient. All drawbacks typical of problem with cohesion are overcome, including eliminating mesh-dependent shear band and artificial plastic zones. Contact sliding intensifies radial plastic flow, which leads to larger reduction in sample thickness. Larger plastic strain and increased pressure in the central region lead to intensification of PT. However, the effect of the reduction in the friction coefficient on PT kinetics is nonmonotonous. Sliding increases away from the center and with growing rotation and is weakly dependent on the kinetic coefficient. Also, cyclic back and forth torsion is studied and compared to unidirectional torsion. Multiple experimental phenomena, e.g., pressure self-multiplication effect, steps (plateaus) at pressure distribution, flow to the center of a sample, and oscillatory pressure distribution for weaker high-pressure phase, are reproduced and interpreted. Reverse PT in high pressure phase that flowed to the low pressure region is revealed. Possible misinterpretation of experimental PT pressure is found. Obtained results represent essential progress toward understanding of strain-induced PTs under compression and shear in RDAC and may be used for designing experiments for synthesis of new high pressure phases and reduction in PT pressure for known phases, as well as for determination of PT kinetics from experiments.