Transient Hygrothermal Stresses Induced in Two-Dimensional Problems by Nonlinear Theory of Coupled Heat and Moisture

According to some experimental data, the value of moisture diffusivity for composite and porous materials is strongly dependent on temperature. Therefore, if the temperature variation of the problem is not confined within a small range, this coefficient may not be regarded as a constant. The purpose of this paper is to study the effect of this temperature-dependent coefficient on the hygrothermal stresses of two-dimensional composite or porous body by nonlinearly coupled hygrothermal theory. In this article, a powerful numerical method, consisting of discretizing the space domain by the finite element method, treating the time domain by Laplace and inverse Laplace transform, and handling the nonlinear term by direct Newton-Raphson iteration, is developed to study the nonlinear coupled transient problem. It can be found from a number of examples that the nonlinear and linear solutions have significant discrepancy in moisture distributions but only a small difference in temperature distributions. In the early stages of the transient period, the induced heat source by rate of moisture based on nonlinear theory is weaker than that based on linear theory. Therefore, the temperature distribution corresponding to linear theory is higher. However, in the latter stage of the transient period, the tendency is the reverse, and the temperature distribution predicted by the nonlinear theory becomes larger.