Mode of a spherical cavity’s thermo-elastodynamic response in a saturated porous medium for non-torsional loads

The thermo-hydro-elastodynamic model (THED), in which the thermo-osmosis and thermal-filtration phenomenon in a two-phase porous thermoelastic medium can be considered, was previously presented by the authors [Ganbin Liu, Kanghe Xie, Rongyue Zheng. Model of nonlinear coupled thermo-hydro-elastodynamics response for a saturated poroelastic medium. Sci China (Ser E) 2009;52(8):2373–83] and is used in this paper to investigate the thermo-elastodynamic response of a spherical cavity in a saturated poroelastic medium when subjected to a time-dependent non-torsional thermal/mechanical source. The Separated Variable Method is introduced, and the non-zero displacement potentials are expanded in terms of the Legendre polynomial. Solutions for the displacement, temperature increment, pore pressure and stress are obtained in the domain of the Laplace transform. Numerical results are also performed for different modes and are compared with the results of the thermoelastic model (TED) to ascertain the validity and the difference between these two models.