A numerical method for the evaluation of non-linear transient moisture flow in cellulosic materials

A numerical method for the transient moisture flow in porous cellulosic materials like paper and wood is presented. The derivation of the model is based on mass conservation for a mixture containing a vapour phase and an adsorbed water phase embedded in a porous solid material. The principle of virtual moisture concentrations in conjunction with a consistent linearization procedure is used to produce the iterative finite element equations. A monolithic solution strategy is chosen in order to solve the coupled non-symmetric equation system. A model for the development of higher order sorption hysteresis is also developed. The model is capable of describing cyclic hardening as well as cyclic softening of the equilibrium water concentration. The model is verified by comparison with the measured response to natural variations in temperature and humidity. A close agreement of the simulated results to measured data is fo