Fractional dual-phase-lag hygrothermoelastic model for a sphere subjected to heat-moisture load

This paper proposes a non-Fourier model of heat and a non-Fick model of moisture diffusion coupling in unification with hygrothermoelasticity theory within the framework of time-fractional calculus theory. The generalized two-temperature theory of hygrothermoelasticity has been used to develop the relevant linearly coupled partial differential equations system. In the context of time-fractional calculus theory, we investigate a hygrothermal elastic problem for a centrally symmetric sphere exposed to physical heat and moisture load at its surface within the limited spherical region. The integral transform approach produces analytical formulas for the transient response of temperature change, moisture distribution, displacement, and stress components in the sphere for pulsed and continuous heat-moisture flux at the sphere's surface. The Gaver-Stehfest procedure is used to invert the analytical hygrothermal variation solutions that were derived in the Laplace domain. The Kuznetsov convergence criterion has studied the problem's stability and bounded variations. The effects of fractional order on the hygrothermal fields and hygrothermoelastic stress response are graphically represented and calculated using numerical data. The specific heat and moisture connection, which abides by Fourier heat conduction and Fick's moisture diffusion, is recovered as a particular case when the fractional-order derivative reduces to the first-order derivative. The study reveals a significant coupling effect between temperature and moisture in composite material T300/5208, with a maximum discrepancy of up to 50%.