Semi-analytical results for transient poroelastic behavior of a functionally graded hollow sphere

This paper provides semi-analytical results for transient poroelastic behaviors of a functionally graded hollow sphere that are lacking in the present literature. The whole medium is theoretically approximated by a spherical multilayer structure. Each layer is treated as a homogeneous spherical shell. The solutions are first explicitly obtained in Laplace space, and then the advanced Stehfest's inversion method is employed to transform these results into the time domain. Numerical examples are provided to demonstrate the validity of the proposed method against the most relevant results given in literature. These validations are for some particular cases where literature results exist, but the capacity of this model is beyond those validation cases. Besides, sensitivity analysis demonstrates the significant impact of radial variations in poroelastic properties on the resulting mechanical fields. These findings are extremely important for validating the correctness and the convergence of sophisticated 3D finite element/finite volume software.