Bending of fluid-saturated linear poroelastic beams with compressible constituents

Analytical solutions are presented for fluid-saturated linear poroelastic beams under pure bending. The stress-free boundary condition at the lateral surfaces is satisfied in the St Venant's sense and the Beltrami-Michell compatibility conditions are resolved rigorously, rendering the flexure of the beams analytically tractable. Two sets of formulations are derived based on the coupled and uncoupled diffusion equations respectively. The analytical solutions are compared with three-dimensional finite element simulations. Both sets of analytical formulations are capable of capturing exactly both the initial (undrained) and the steady-state (fully drained) deflection of the beams. However, the analytical solutions are found to be deficient during the transient phase. The cause for the deficiency of the transient analytical solutions is discussed. The accuracy of the analytical solutions improves as Poisson's ratio and the compressibility of the constituents of the porous beam increase, where the St Venant's edge effect at the lateral surfaces is mitigated.