Development of a hysteresis model based on axisymmetric and homotopic properties to predict moisture transfer in building materials

Abstract

Current hygrothermal behaviour prediction models neglect the hysteresis phenomenon. This leads to a discrepancy between numerical and experimental results, and a miscalculation of buildings’ durability. In this paper, a new mathematical model of hysteresis is proposed and implemented in a hygrothermal model to reduce this discrepancy. The model is based on a symmetry property between sorption curves and uses also a homotopic transformation relative to a parameter $s\in [0,1]$ . The advantage of this model lies in its ease of use and implementation since it could be applied with the knowledge of only one main sorption curve by considering $s=0$ , in other words, we only use the axisymmetric property here. In the case where the other main sorption curve is known, we use this curve to incorporate the homotopy property in order to calibrate the parameter $s$ .The full version of the proposed model is called Axisymmetric + Homotopic. Furthermore, it was compared not only with the experimental sorption curves of different types of materials but also with a model that is well known in the literature (CARMELIET’s model). This comparison shows that the Axisymmetric + Homotopic model reliably predicts hysteresis loops of various types of materials even with the knowledge of only one of the main sorption curves. However, the full version of Axisymmetric + Homotopic model is more reliable and covers a large range of materials. The proposed model was incorporated into the mass transfer model. The simulation results strongly match the experimental ones.