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Semicrystalline thermoplastic polymers have superior mechanical properties and are thus very important in numerous technically relevant applications. During the thermoforming process of parts made of thermoplastic polymers the "springback effect", i.e. the undesired distortion of a part after unloading and removal from tooling, depicts a major problem. These shape distortions occur due to the formation of residual stresses. To counteract this effect, time-consuming and cost-intensive trial and error approaches are typically conducted to carefully determine the optimal set of process parameters. Hence, a strong demand for computational models, which accurately predict the material and structural response of the part during forming, arises. Therefore, a phenomenological model formulation is proposed in this work, which is valid for large deformations and large deformation rates in the context of isothermal processes. To capture the biphasic nature of the polymer, i.e. to account for the amorphous and semicrystalline regions of the underlying microstructure, a parallel arrangement of both phases is applied. The overall material response is obtained by a rule of mixture. The qualitative validation of the hyperelastic, viscoplastic material model shows the promising potential to predict the formation and relaxation of residual stresses during the forming process of thermoplastic polymers.