Lithium-ion batteries with silicon-graphite composite anodes feature an asymmetric and direction-dependent voltage hysteresis. Upon comparing established hysteresis models from literature, it was found that a separate modelling of charge and discharge direction is required for both the operator-based Preisach model and the differential equation-based one-state model, often referred to as Plett model. This paper presents the first bidirectional implementation of the one-state hysteresis model based on extensive measurements of first-order reversal branches of a Si/C NMC cell. The approach accounts for directionality but cannot deal with the complexity of the hysteresis traverses, so an extension of the Preisach model is discussed and found to be infeasible. This justifies the development of a novel hysteresis model, the trajectory correction hysteresis (TCH) model, that fulfils the identified requirements for bidirectionality, closed-loop property and direct data fit and can be generally applied to any cell chemistry. The TCH model considers the traverse starting point, which allows for the unambiguous definition of hysteresis states and enables the simulation of complex trajectories due to two correction mechanisms. The static and dynamic current profiles in complex hysteresis scenarios demonstrate superior performance with 4.5 mV mae compared to Preisach (19.6 mV mae) and Plett (11.7 mV mae) models.