A finite element model for poroelastic beams with axial diffusion

The finite element method is used for those fluid-saturated poroelastic rods in which diffusion is possible only in the axial direction as a result of the microgeometry of the solid skeleton material. Variational principles are developed first for this purpose. Two types of variables, the displacements and pore pressure, are involved in the time dependent functionals. The method of Lagrange multipliers is employed in order to include the flow equations (generalized Darcy’s law) into the Euler–Lagrange equations of the functionals. A mixed finite element scheme is then presented based on one of the variational functionals obtained. Numerical solutions for both types of variables are found to coincide well with the existing analytical solutions. Some interesting results are demonstrated which are not available by analytical methods.