A bipolar charge transport model has first been used to compare the current voltage characteristics (J-E) for different applied voltage protocols and different times under voltage taking low density polyethylene as a case study, as a steady state may take a very long time to be reached experimentally. Simulation results highlight the necessity to spend substantial time under voltage to reach a quasi-stable current. In a second part, evolutions of the model in terms of physical processes are proposed, to observe their impact on the J-E characteristics, and particularly the appearance of electric field thresholds, as proposed by the Space Charge Limited Current (SCLC) theory. To do so, different mathematical expressions are proposed for each physical process related to injection, mobility and trapping. Field dependent mobility equations allow obtaining electric field threshold values comparable to experimental data, while a constant mobility is the only way to observe a trap free limit region. Moreover, all parameters linked to trapping are of most importance in the observation of a SCLC characteristic, but are not enough to observe a trap free limit region when electric field dependent mobility is considered.