Stabilized Low-Order Explicit Finite Element Formulations for the Coupled Hydro-Mechanical Analysis of Saturated Poroelastic Media

Abstract

We developed new stabilized low-order explicit finite element formulations for analysing the fully coupled hydro-mechanical behaviour of fluid-saturated poroelastic media. For space stabilization, the low-order U-p finite element employs two stabilization schemes. One stabilization scheme is based on the polynomial pressure projection technique in the fluid phase. The other one assumes enhanced strain field for the solid-phase terms. For time stabilization, an unconditionally stable explicit integration formula is proposed for discretization in the time domain to eliminate the time-step-size sensitivity of the temporal discretization finite difference format. The performance of the proposed formulations is demonstrated through four numerical examples. The proposed formulations not only agree strongly with the analytical/reference solutions, but also yield unconditionally stable high-precision results that outperform the standard finite element combined finite difference scheme. The modelling results indicate the proposed schemes possess significant advantages in terms of precision and computational efficiency for large timescales and adaptability to space-domain discretization. The proposed schemes have great potential in engineering applications for large timescale problems.