A finite element method for nonlinear and fully coupled transient hygrothermal transfer

A fully coupling nonlinear finite element algorithm for moisture and heat transfer is developed and implemented. The finite element model starts from a suitable formulation of the constitutive and equilibrium equations. The nonlinearity arises due to the strong moisture and temperature dependence of the material properties. Four examples are presented to check the validity and precision of the finite element model. Two of the examples compare the numerical results with simplified, one-dimensional analytical solutions. Perfect agreement is obtained between the analytical and numerical solutions. The results show that the dependency of the material coefficients on the moisture and temperature is important, even for one-dimensional cases. The other two examples, without direct analytical solution due to the material nonlinearity, show that the fully coupling between the moisture and heat conduction is essential. The formulation can be used for the transient analysis of moisture and heat conduction with arbitrary geometrical dimensions and time-dependent loading conditions.