Real cloth exhibits bending effects, such as residual curvatures and permanent wrinkles. These are typically explained by bending plastic deformation due to internal friction in the fibre and yarn structure. Internal friction also gives rise to energy dissipation which significantly affects cloth dynamic behaviour. In textile research, hysteresis is used to analyse these effects, and can be modelled using complex friction terms at the fabric geometric structure level. The hysteresis loop is central to the modelling and understanding of elastic and inelastic (plastic) behaviour, and is often measured as a physical characteristic to analyse and predict fabric behaviour. However, in cloth simulation in computer graphics the use of hysteresis to capture these effects has not been reported so far. Existing approaches have typically used plasticity models for simulating plastic deformation. In this paper, we report on our investigation into experiments using a simple mathematical approximation to an ideal hysteresis loop at a high level to capture the previously mentioned effects. Fatigue weakening effects during repeated flexural deformation are also considered based on the hysteresis model. Comparisons with previous bending models and plasticity methods are provided to point out differences and advantages. The method requires only incremental extra computation time.