This paper presents a 3D thermomechanical constitutive model for polycarbonate (PC) polymers, aiming to predict the material characteristics of PC under complex thermomechanical boundary and strong impact loading conditions. The model is applied to simulate the high-velocity ballistic impact tests. Quasi-static tension, Split-Hopkinson Tension Bar (SHTB), and ballistic impact tests are carried out to experimentally investigate the thermomechanical behavior of PC. Fundamental characteristics of PC, such as the transient yield peak, the post-yield softening and the subsequent hardening, are characterized by introducing two scalar and one tensorial internal variables. Constitutive equations, specifically, (i) the plastic flow rule; (ii) the evolution equations associated with the internal variables; (iii) the temperature evolution; (iv) the strain rate, temperature and pressure-dependent yield limit are derived within a thermodynamically consistent framework. The model is then implemented into the finite element software ABAQUS/Explicit by means of a user-defined material subroutine VUMAT. Finally, numerical simulations are carried out and validated against experimental data. Finite element simulations of the ballistic tests well demonstrate the capabilities of the proposed model to accurately predict thermomechanical behavior of PC undergoing high-velocity impact loadings. POLYM. ENG. SCI., 58:2237-2248, 2018. (c) 2018 Society of Plastics Engineers