In the automotive field, it is important to predict materials behavior and thereby the components behavior with high accuracy. The first part of paper deals with a complete experimental characterization both for quasi-static and dynamic loadings. In quasi static, we carried out trials at three different temperatures (-40°C, 23°C and 80°C) for which, each time, three different levels of hygrometry (RH=0%, RH=50% and RH=85%) have been imposed. In dynamic, we tested the fabric for four different levels of strain rate (from 10 -3 /s up to 400/s) at the ambient temperature (23°C) and for three same previous levels of hygrometry. The second part of the paper deals with the writing of an adapted constitutive law for the fabric. Thanks to [1-2], we developed and implement a new law which is able to take into account the evolutions of elastic strains, irreversible strains and damages, the strain rate sensitivity and the hygrometry effect.